SOLUTION: Prove that if a,b, and c are a pythagorean triple, then ka, kb, and kc (where k>0) represent the side lengths of a right triangle.

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Question 259997: Prove that if a,b, and c are a pythagorean triple, then ka, kb, and kc (where k>0) represent the side lengths of a right triangle.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that if a,b, and c are a pythagorean triple, then ka, kb, and kc (where k>0) represent the side lengths of a right triangle.

Since a,b and c are a Pythagorean triple,

a%5E2%2Bb%5E2=c%5E2

Multiply both sides by by k%5E2

k%5E2a%5E2%2Bk%5E2b%5E2=k%5E2c%5E2

That can be written as 

%28ka%29%5E2+%2B+%28kb%29%5E2=%28kc%29%5E2

which proves that ka, kb, and kc also
satisfy the Pythagorean theorem equation and
therefore can be side lengths of a right 
triangle. 

Edwin