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