The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. find the lengths of the three sides of the triangle.

suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8
use the pythagorean theorem:
x^2+(2x+8)^2=(3x-8)^2
x^2+(4x^2+32x+64)=(9x^2-48x+64)
4x^2-80x=0
x=0 or x=20
so the sides are 20, 48, and 52