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.
<pre><font size =4 color = "indigo"><b>
Since a,b and c are a Pythagorean triple,

{{{a^2+b^2=c^2}}}

Multiply both sides by by {{{k^2}}}

{{{k^2a^2+k^2b^2=k^2c^2}}}

That can be written as 

{{{(ka)^2 + (kb)^2=(kc)^2}}}

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

Edwin</pre>