SOLUTION: Suppose the measures of the two legs of a right triangle differ by 2 inches and that the hypotenuse is 2 inches longer than the longer leg. Find the measures of the three sides.

Algebra ->  Triangles -> SOLUTION: Suppose the measures of the two legs of a right triangle differ by 2 inches and that the hypotenuse is 2 inches longer than the longer leg. Find the measures of the three sides.       Log On


   

Question 942809: Suppose the measures of the two legs of a right triangle differ by 2 inches and that the hypotenuse is 2 inches longer than the longer leg. Find the measures of the three sides.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So the legs would be x and x-2 and the hypotenuse would be x%2B2.
Use the Pythagorean theorem,
%28x%2B2%29%5E2=x%5E2%2B%28x-2%29%5E2
x%5E2%2B4x%2B4=x%5E2%2Bx%5E2-4x%2B4
x%5E2%2B4x%2B4=2x%5E2-4x%2B4
x%5E2-8x=0
x%28x-8%29=0
Only non-zero solutions make sense here,
x-8=0
x=8
So the lengths are 6,8, and 10.