In a 45-45-90 triangle where the hypotenuse is y and the other two sides are 13 square root x, how do you solve for x?

Question

 In a 45-45-90 triangle where the hypotenuse is y and the other two sides are 13 square root x, how do you solve for x?

Answer 1

If the hypotenuse is y in an isosceles right triangle, then each leg measures y/√2.

 

Now you have y/√2 = 13/√x, using the latter expression as the given side length.

 

Manipulate this by various algebraic operations to solve for x (in terms of y squared)!