Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Created by @bmtran (Bryant Tran)

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t> is the perimeter of a right angle triangle with integral length sides, {</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>a</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>b</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>c</w:t></w:r><w:r><w:t> }, there are exactly three solutions for</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t> = 120.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>{[20,48,52], [24,45,51], [30,40,50]}</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given any value of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t>, return a cell array whose elements are the sorted side lengths of a possible right triangle whose perimeter is</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t>. Furthermore, the elements of the output should be sorted by their shortest side length.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

1402 Solutions
322 Solvers

Last Solution submitted on Sep 20, 2020

Last 200 Solutions

Problem Comments

Solution Comments

Solution 2813128

1 Comment

1 Comment

Sergio Enrique Pinto Castillo on 9 Aug 2020

I think, the statement of the problem is not complete. The reference problem is not available. I know very well about right angle triangles but I do not have the idea on how to find the solutions. Please help me out.

Solution 2593735

1 Comment

1 Comment

Piero Cimule on 22 Jun 2020

c=[];
for A=1:p
B=0;
while B < 1000
B = B+1;
C = sqrt((A^2) + (B^2));
perimeter = A+B+C;
if perimeter==p
c(end+1,:) = [A,B,C];
end
end
end
c=unique(sort(c,2),'rows');
x=cell(1,size(c,1));
for i=1:size(c,1)
[x{1,i}]= deal(c(i,:))
end
c=x

Solution 2055983

1 Comment

1 Comment

Miles Walker on 12 Dec 2019

Works, but is horribly inefficient especially for higher p...

Solution 174395

1 Comment

1 Comment

Aurelien Queffurust on 18 Dec 2012

solution using a Neural Network Toolbox function ;)

Problem Recent Solvers322

Problem Tags

plus15 projecteuler

Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers322

Suggested Problems

More from this Author56

Problem Tags

Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers322

Suggested Problems

More from this Author56

Problem Tags

Players