SOLUTION: I need help with this question. 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.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this question. 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.       Log On


   

Question 207494: I need help with this question.
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

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x=shorter leg

by Pythagoras ___ x^2 + (2x + 8)^2 = (3x - 8)^2

x^2 + 4x^2 + 32x + 64 = 9x^2 - 48x + 64

0 = 4x^2 - 80x = x^2 - 20x = x (x - 20)

x = 0 ___ not a realistic solution

x - 20 = 0 ___ x = 20

longer leg ___ 2(20) + 8 ___ 48

hypot ___ 3(20) - 8 ___ 52