SOLUTION: I've been stuck on this problem for a long time, and I REALLY need some help! The question is: "The longer leg of a right triangle is 4 feet longer than the other leg. Find the l

Algebra ->  Pythagorean-theorem -> SOLUTION: I've been stuck on this problem for a long time, and I REALLY need some help! The question is: "The longer leg of a right triangle is 4 feet longer than the other leg. Find the l      Log On


   

Question 562716: I've been stuck on this problem for a long time, and I REALLY need some help!
The question is:
"The longer leg of a right triangle is 4 feet longer than the other leg. Find the length of the two legs if the hypotenuse is 20 feet." I know that you set it up like this: x^2+(x+4)^2=20.
I need to show work, but I don't really know what I'm doing.
Answer by issacodegard(60) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, your right about how to set it up! So I'll work out the steps,
x%5E2%2B%28x%2B4%29%5E2=20
Expand using FOIL:
x%5E2%2Bx%5E2%2B4x%2B4x%2B4%5E2=20
Simplify:
2x%5E2%2B8x%2B16=20
x%5E2%2B4x%2B8=10
x%5E2%2B4x-2=0
Use the quadratic formula:
x=%28-4%2B-sqrt%284%5E2-4%2A1%2A%28-2%29%29%29%2F%282%2A1%29
x=%28-4%2B-sqrt%2824%29%29%2F2
x=%28-4%2B-sqrt%286%29%2A2%29%2F2
x=-2%2B-sqrt%286%29
Since x represents a distance, we know x>=0. So, the length of the first leg is
x=-2%2Bsqrt%286%29
And, the second leg has length,
x%2B4=2%2Bsqrt%286%29