SOLUTION: 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

Algebra ->  Triangles -> SOLUTION: 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      Log On


   

Question 308612: 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.
I already know the formula, I can't work it out. I don't know how.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
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.
let the shorter leg be x
3times shorter leg = 3x
8 feet less than 3 times shorter leg = 3x-8
Hypotenuse = 3x-8
.
2 times shorter leg = 2x
8 feet more than 2 times shorter leg
longer leg =2x+8
.
x^2+(2x+8)^2= (3x-8)^2
x^2+4x^2+32x+64 = 9x^2-48x+64
4x^2-80x=0
4x(x-20)=0
x=20 feet
shorter leg = x
longer leg = 2x+8
=40+8
=48 feet
.
hypotenuse = 3x-8
= 60-8
= 52 feet
.
20^+48^2= 52^2
2704 = 2704