# Thread: Consider a right triangle with integer sides...

1. ## Consider a right triangle with integer sides...

Consider a right triangle with integer sides having no common factor. Show that the average of the odd leg and the hypotenuse is a square number.

2. Originally Posted by NikoBellic
Consider a right triangle with integer sides having no common factor. Show that the average of the odd leg and the hypotenuse is a square number.
The odd leg of a right triangle is of the form $m^2-n^2$ and in your case $(m,n)=1$. The hypotenuse of the same triangle is then $m^2+n^2$.

Now what is $\frac{(m^2+n^2)+(m^2-n^2)}{2}$?