SOLUTION: a right triangle has a hypotenuse that is 59 miles long. One side is 1.05 longer than the other. What are the lengths of the two legs

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Question 857417: a right triangle has a hypotenuse that is 59 miles long. One side is 1.05 longer than the other. What are the lengths of the two legs
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a right triangle has a hypotenuse that is 59 miles long. One side is 1.05 longer than the other. What are the lengths of the two legs
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x%5E2+%2B+%28x%2B1.05%29%5E2+=+59%5E2+=+3481
2x%5E2+%2B+2.1x+%2B+1.1025+=+3481
2x%5E2+%2B+2.1x+-+3479.8975+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2.1x%2B-3479.8975+=+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=%282.1%29%5E2-4%2A2%2A-3479.8975=27843.59.

Discriminant d=27843.59 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2.1%2B-sqrt%28+27843.59+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282.1%29%2Bsqrt%28+27843.59+%29%29%2F2%5C2+=+41.1909966319876
x%5B2%5D+=+%28-%282.1%29-sqrt%28+27843.59+%29%29%2F2%5C2+=+-42.2409966319876

Quadratic expression 2x%5E2%2B2.1x%2B-3479.8975 can be factored:
2x%5E2%2B2.1x%2B-3479.8975+=+%28x-41.1909966319876%29%2A%28x--42.2409966319876%29
Again, the answer is: 41.1909966319876, -42.2409966319876. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2.1%2Ax%2B-3479.8975+%29

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x =~ 41.191 miles (the short leg)
x + 1.05 =~ 42.241 miles