Question 22895
Right triangle formula is a^2 + b^2 = c^2.


(x)^2 + (x-4)^2 = (20)^2
x^2 + x^2 -8x +16 = 400
2x^2 -8x + 16 = 400
2(x^2-4x+8) = 400
x^2-4x+8 = 200
x^2-4x-192 = 0
(x-16)(x+12) =0


The solutions for x are 16 and -12.  We can ignore the -12 answer. So, x=16 and the shorter leg is x-4 or 12.


I hope that you were able to follow the solution.