SOLUTION: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.

Algebra ->  Surface-area -> SOLUTION: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.       Log On


   

Question 206204: The area of a right triangle is 120 sq. in. The longer leg is 4 more than twice the shorter leg. Find the length of each leg. Show all work to receive credit.

Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
For a triangle, A=%281%2F2%29bh
Because it is a right triangle, the two legs are the base and height.
let x = the shorter leg
2x+4 = the longer leg
120+=+%281%2F2%29%28x%29%282x%2B4%29
240=2x%5E2%2B4x
2x%5E2%2B4x-240=0
Divide by 2.
x%5E2%2B2x-120=0
Factor.
%28x%2B12%29%28x-10%29=0
%28x%2B12%29=0 or %28x-10%29=0
x=-12 or x=10
The side length canot be negative, so ignore x=-12


The shorter leg has length 10in, and the longer leg has length 2%2810%29%2B4 = 24in