SOLUTION: The longer leg of a right triangle is 1 inch longer than the shorter leg. The hypotenuse is 9 inches longer than the shorter leg. Find the side length of the triangle.

Question 1049180: The longer leg of a right triangle is 1 inch longer than the shorter leg. The hypotenuse is 9 inches longer than the shorter leg. Find the side length of the triangle.
Answer by jorel555(1290) (Show Source): You can put this solution on YOUR website!
Let n be the length of the shortest leg. Then the other leg is n+1; and the hypotenuse is n+9. So:
n�+(n+1)�=(n+9)�
2n�+2n+1=n�+18n+81
n�-16n-80=0
(n-20)(n+4)=0
n=20 or -4
Throwing out the negative result, we get the length of the shorter leg to be 20 inches, the longer leg to be 21 inches, and the hypotenuse is 29 inches. ☺☺☺☺
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