How to find the largest square inside a triangle?

I am wondering how you would go about to find the largest square that would fit inside a triangle?

An example of what i am asking is:

What is the side length of the largest square that would fit inside a right angled triangle with the sides 5,12, and 13?

Any help would be appreciated

Medusa

Re: How to find the largest square inside a triangle?

Quote:

Originally Posted by

**johnny** The largest rectangle that would fit inside a right triangle with the sides 5, 12, 13 is a square. Let the square have side x. By Pythagorean theorem, $\displaystyle (12\,-\,x)^2\,+\,x^2\,=\,(13\,-\,\sqrt{2x^2\,-\,10x\,+\,25})^2.$ Solving the equation gives x = 60/17.

Or simply (a=5, b=12) x = ab / (a + b) ; (product of legs) / (sum of legs)