SOLUTION: Could I have some help on the following problem, can't seem to solve. The hypotenuse of a triangle is 10ft long. The longer one is two feet longer than the other. Find the length o

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Question 190580: Could I have some help on the following problem, can't seem to solve. The hypotenuse of a triangle is 10ft long. The longer one is two feet longer than the other. Find the length of the shorter leg.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the length of the shorter leg, then the longer leg is x+2.
Using the Pythagorean theorem c%5E2+=+a%5E2%2Bb%5E2, we can write:
10%5E2+=+x%5E2%2B%28x%2B2%29%5E2 Simplifying, we get:
100+=+2x%5E2%2B4x%2B4 Subtracting 100 from both sides and rearranging, we have:
2x%5E2%2B4x-96+=+0 This can be factored into...
2%28x%5E2%2B2x-48%29+=+0 so...
x%5E2%2B2x-48+=+0 Factor this into...
%28x-6%29%28x%2B8%29+=+0 Applying the zero product rule...
x-6+=+0 or x%2B8+=+0 so that...
x+=+6 or x+=+-8 Discard the negative solution as lengths are positive quantities.
x+=+6
The shorter leg is 6 feet.