SOLUTION: The hypontenuse of a right triangle is 15 meters. If one leg is 3 meters longer than the other, then what are the lengths of the legs?

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Question 148012: The hypontenuse of a right triangle is 15 meters. If one leg is 3 meters longer than the other, then what are the lengths of the legs?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The hypontenuse of a right triangle is 15 meters. If one leg is 3 meters longer than the other, then what are the lengths of the legs?
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Short leg = S
s%5E2+%2B+%28s%2B3%29%5E2+=+15%5E2
s%5E2+%2B+s%5E2+%2B+6s+%2B+9+=+225
2s%5E2+%2B+6s+-216+=+0
s%5E2+%2B+3s+-+108+=+0
(s+12)*(s-9) = 0
s = 9, s = -12
Negative lengths don't work, so discard that.
s = 9
2nd side = 12
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Or, use quadratic instead of factoring
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-108+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-108=441.

Discriminant d=441 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+441+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+441+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%283%29-sqrt%28+441+%29%29%2F2%5C1+=+-12

Quadratic expression 1x%5E2%2B3x%2B-108 can be factored:
1x%5E2%2B3x%2B-108+=+%28x-9%29%2A%28x--12%29
Again, the answer is: 9, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-108+%29