Problem 52819. Easy Sequences 30: Nearly Pythagorean Triangles

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A Nearly Pythagorean Triangle (abbreviated as \"NPT'), is an i</w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>nteger-sided </w:t></w:r><w:r><w:t>triangle whose square of the longest side, which we will call as its 'hypotenuse', is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>1</w:t></w:r></w:customXml><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:u/></w:rPr><w:t>more</w:t></w:r><w:r><w:t> than the sum of square of the shorter sides. This means that if </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>c</w:t></w:r></w:customXml><w:r><w:t> is the hypotenuse and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> are the shorter sides, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t>, satisfies the following equation: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>c^2 = a^2+b^2+1</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t> where: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a \\le b &lt; c</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The smallest </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t> is the triangle </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[2,2,3]</w:t></w:r></w:customXml><w:r><w:t>, with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>3^2=2^2+2^2+1</w:t></w:r></w:customXml><w:r><w:t>. Other examples are </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[4,8,9]</w:t></w:r></w:customXml><w:r><w:t>, </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[18,30,35]</w:t></w:r></w:customXml><w:r><w:t>, and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[649,1080,1260]</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Unfortunately, unlike Pythagorean Triangles, a 'closed formula' for generating all possible </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t>'s, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t>'s with a known ratio of the shorter sides: </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r = b/a</w:t></w:r></w:customXml><w:r><w:t>. </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Given the value of </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t>, find the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:rPr><w:b/></w:rPr><w:t> with the </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>second smallest</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> perimeter. </w:t></w:r><w:r><w:t>For example for </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>r = 2</w:t></w:r></w:customXml><w:r><w:t>, that is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>b = 2a</w:t></w:r></w:customXml><w:r><w:t>, the smallest perimeter is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>21</w:t></w:r></w:customXml><w:r><w:t>, while the second smallest perimeter is </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>377</w:t></w:r></w:customXml><w:r><w:t>, for the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t> with dimensions </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[72,144,161]</w:t></w:r></w:customXml><w:r><w:t>. Please present your output as vector </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>[a,b,c]</w:t></w:r></w:customXml><w:r><w:t>, where </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> is the smallest side of the </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>NPT</w:t></w:r></w:customXml><w:r><w:t>, and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>c</w:t></w:r></w:customXml><w:r><w:t> is the hypotenuse.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 318px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an i<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">nteger-sided <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">triangle whose square of the longest side, which we will call as its 'hypotenuse', is 1<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">more<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> than the sum of square of the shorter sides. This means that if c<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> is the hypotenuse and a<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> and b<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> are the shorter sides, <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, satisfies the following equation: </div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> <img src="data:image/png;base64,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" width="99.5" height="19" style="width: 99.5px; height: 19px;"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> where: <img src="data:image/png;base64,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" width="62" height="18" style="width: 62px; height: 18px;"></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">The smallest <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> is the triangle <img src="data:image/png;base64,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" width="48.5" height="19" style="width: 48.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, with <img src="data:image/png;base64,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" width="100.5" height="19" style="width: 100.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. Other examples are <img src="data:image/png;base64,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" width="48.5" height="19" style="width: 48.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, <img src="data:image/png;base64,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" width="71" height="19" style="width: 71px; 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height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. </div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Unfortunately, unlike Pythagorean Triangles, a 'closed formula' for generating all possible <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">'s, has not yet been discovered, at the time of this writing. For this exercise, we will be dealing with <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">'s with a known ratio of the shorter sides: <img src="data:image/png;base64,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" width="50.5" height="19" style="width: 50.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. </div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">Given the value of r<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, find the <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAkCAYAAAA9+eyvAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAQqADAAQAAAABAAAAJAAAAAD+3wP6AAAEPklEQVRoBe1Xa2iOYRj+NrLI+ZBjGiN/nJUh5JBSJCzlUPaLcijlhyW0zQ/80BJGDmWK5AfjB5vRbDVmfpCVTZgtOa1QjsPmcF167rp7PO/7fu+3b/nz3nXtuQ/Xfb/Pe7/P4VssFknUgagDUQeiDkQdiDoQsgMpAfwMxO8CnSzeDNh1lk/Mq1AYtyUHjmPAHOACYNeE66+04G8j0AA8BZjzBtByDUamdoTUD4O/M2ROrA8StgK/FVjIT8Yh2Aowhy80BdDSFUYBoGs+gL0O2AJcUbF30FcDIj2gSO026NUA57MXqAJ0zTzYuwA27isgsWzoCcsdZEqhj9C7B1Tii5Gf5cGbb+JSc6rF22zFp5v4EuOvwTjY+GQ4bmKsydWkpSeMRwBjQ3QgjN4Z5A+ATJrjBp8C/OLfgPcAc12yHU6p1wzd3qa0uZqEswc65RDwDOhGw5JG2MIvtGI084GHDn8s1eV0+Ljn2VG+nIhfI2aBlAaUAFy+LuGKECmDwhfQQrteOYQ/Dz7uby51LaNgpCtHqdJF5Za6IUYiI78GJ7YIkP1Jmy/skv1wMr7KFYSPX5NNJYdYA7jkPpzCqTSEERhTHOSNivsdumvrjoE/HUhY7iGTJzcnwBNfJncOuktq4eRK6OsKwseGSo1f0Ac4eDwUfyreNgdHu4oVt1wHkqUPQiFO9qwpyKUpL/ED+kDjl4EHGOO3xOEYDxoOebyeXcKzQJ7zGfpQF8n47DMsx4ebcGgtMjmhbFWhzvjo36H8VIXPfewljxGQl9xtkfrDPqri/AjLLY5t8gyTehwn2IRk2Fz+LK6/iL7aniOmfxydMfzJGF0yEk49aZ4Dp4GLQBXAVSbx29AXAEGSB4LkvAoiJxJPRdJbwL5yeIN8AuThS6FTeIbwKnxtdAz/CG8byWuBXgHUAvXATaAIyAfkloAaKNyGUrMokJ0AIdM84IAj94iJcQJlJj7R+E4Z2zVcNhzmXXIRQvp6gd8KSCNWhsyPi55rHsBT3paxcMjDuY9HAzzZ6VsBuKQLnHol8cprr3A1yjx4y/Rrb0FXfjWc3LOuO5n8CkAmUQCdP1b4dfiVXDIXTuFzzHCRQvoKVc2akLlx0dlZdrjSh80vLy8mP5D8+PsUv8GnbpjQE1XTvoHirsPD0EsWI8D4dS8C/MWAnNJphlfiw1+oYnKuKFdoNR0Z/GktUipKMkdeZ/za0wKK5hqerIzxHnz5oSW8LA9eGPd69ewv0PU1HqaOJ3c4InKf8/8CP+ELCveFD1Ffm2wG89or5SggjeVvkKRKb1TjspUHcIukBDzhvOGf8OBx+TYZjtTV28QjzdPNwzvfqtcIe5hnRsjATPDl68qEOTYDfs2YjTh5ywBb9O8NXZN6k02Owz4JThtg1xL7JWKT4qjTYZRNqOx1zXbYQ6PCUQeiDkQdiDoQdSDqQNSB/92BP9fQRStWxlTRAAAAAElFTkSuQmCC" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> with the <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">second smallest<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> perimeter. <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">For example for <img src="data:image/png;base64,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" width="35.5" height="18" style="width: 35.5px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, that is <img src="data:image/png;base64,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" width="44" height="18" style="width: 44px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, the smallest perimeter is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAJKADAAQAAAABAAAAJAAAAAAqDuP8AAAB/0lEQVRYCe2WSytFURSAr2eXxMCAQt1QRowwUVIeIwyVgbo/wS9gYMIAExNMTCmPkoGpUiiUTJTHhDwmN/JW+FadfdudzmOf455Mzqqvvfbaa6+9ztr77HMSiVjiCsQViLYCBT7hGxjvhxEYhEp4gQwEkRTOY3AIrxBYipgxDp/w48ASNr+HwSVRB/Og4jSKMYwsMskpEd22jk+xS/Aa7HPwAfqcUAn1WkFOabshCRXQByegLyDb6SSrGCdAtvoL1JxQCW0T4BqqwC4lGM5BLTBrd3Doy4Mp/8AJlTFZyjzsEFiZ5KnVAkfK6NHuaf6+CeXbAtXT34EVm13vHmudb03PiVpoiyJnRM6Ql7xrg5eanhPVXiGToCnNaUPTc6KGSWjAWvmedi0nWfwhSClzH0AO9ZBhnECH2jBm1m0KTZJZzlr8lcgSamVtueQOQO4jU4kkoVpWv4ELqDbNxPILlJDJoS4n8KYVvIf2ztIjaez3kH0R2RpJRr7anXAF/ybyC7IFT9DmkUWasXaP8UBb5hZHtlLepDfoAjeRqsnN3eTmgH0f1LfP91vmtGV5BFgAuWduIW1BkxVJuBlaYBfOwE30v4akm5OXfYZB9UQmrXz9nUT+KEdBjzFNX46CsXTgqQfw0zP4O91Jk9ifXWI9Ypd/pFjiCsQViCsQV8CkAr/vVI4QpQlS3QAAAABJRU5ErkJggg==" width="18" height="18" style="width: 18px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, while the second smallest perimeter is <img src="data:image/png;base64,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" width="25.5" height="18" style="width: 25.5px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, for the <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> with dimensions <img src="data:image/png;base64,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" width="86" height="19" style="width: 86px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">. Please present your output as vector <img src="data:image/png;base64,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" width="47.5" height="19" style="width: 47.5px; height: 19px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, where a<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> is the smallest side of the <img src="data:image/png;base64,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" width="33" height="18" style="width: 33px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; ">, and c<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "> is the hypotenuse.</div></div></div>

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Problem 52819. Easy Sequences 30: Nearly Pythagorean Triangles

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Problem 52819. Easy Sequences 30: Nearly Pythagorean Triangles

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