SOLUTION: The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the hypotenuse is 22 inches more than twice the length of

Algebra ->  Triangles -> SOLUTION: The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the hypotenuse is 22 inches more than twice the length of      Log On


   

Question 945496: The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. Find the side lengths of the triangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Pythagorean theorem,
L%5E2%2B%282L%2B20%29%5E2=%282L%2B22%29%5E2
L%5E2%2B4L%5E2%2B80L%2B400=4L%5E2%2B88L%2B484
L%5E2-8L-84=0
%28L-14%29%28L%2B6%29=0
Use only the positive solution.
L-14=0
L=14
So then,
L%5B2%5D=20%2B2%2814%29
L%5B2%5D=20%2B28
L%5B2%5D=48
and
L%5B3%5D=22%2B2%2814%29
L%5B3%5D=22%2B28
L%5B3%5D=50