SOLUTION: The sides of a right triangle have lengths (x-5), (x+2), and (x+3). Find the value of x and the length of each side.

Algebra ->  Triangles -> SOLUTION: The sides of a right triangle have lengths (x-5), (x+2), and (x+3). Find the value of x and the length of each side.       Log On


   

Question 846776: The sides of a right triangle have lengths (x-5), (x+2), and (x+3). Find the value of x and the length of each side.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem,
%28x%2B3%29%5E2=%28x-5%29%5E2%2B%28x%2B2%29%5E2
x%5E2%2B6x%2B9=x%5E2-10x%2B25%2Bx%5E2%2B4x%2B4
x%5E2%2B6x%2B9=2x%5E2-6x%2B29
x%5E2-12x%2B20=0
%28x-2%29%28x-10%29=0
Two solutions:
x-2=0
x=2
The sides would then be -3,0,and 5.
This is not a good solution.
x-10=0
x=10
The sides would then be 5,12,and 13.
This is a good solution.