SOLUTION: The sides of a right triangle are x, x+31, and x+32 units long. Find the side lengths of the triangle by solving for x.

Algebra ->  Triangles -> SOLUTION: The sides of a right triangle are x, x+31, and x+32 units long. Find the side lengths of the triangle by solving for x.       Log On


   

Question 952730: The sides of a right triangle are x, x+31, and x+32 units long. Find the side lengths of the triangle by solving for x.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

in a right triangle:c%5E2=a%5E2%2Bb%5E2

if the sides of a right triangle are x, x%2B31, and x%2B32 units long, then we have
%28x%2B32%29%5E2=x%5E2%2B%28x%2B31%29%5E2
x%5E2%2B64x%2B32%5E2=x%5E2%2Bx%5E2%2B62x%2B31%5E2
x%5E2%2B64x%2B1024=2x%5E2%2B62x%2B961
0=2x%5E2-x%5E2%2B62x-64x%2B961-1024
x%5E2-2x-63=0
x%5E2%2B7x-9x-63=0
%28x%5E2%2B7x%29-%289x%2B63%29=0
x%28x%2B7%29-9%28x%2B7%29=0
%28x%2B7%29%28x-9%29=0
solutions:
if %28x%2B7%29=0=>x=-7...disregard negative solution, side the length must be positive
if +%28x-9%29=0=>highlight%28x=9%29-> your answer
so, now we can find the length of all three sides:
highlight%28x=9%29
highlight%28x%2B31=40%29
highlight%28x%2B32=41%29

check if they are the sides of a right-angle triangle:
%28x%2B32%29%5E2=x%5E2%2B%28x%2B31%29%5E2
41%5E2=9%5E2%2B40%5E2
1681=81%2B1600
1681=1681...which verifies our answer