SOLUTION: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16cm long,how long is the length of the hypotenuse?

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Question 357042: The hypotenuse of a right triangle is 4cm less than twice as long as one of the other side. If the third side is 16cm long,how long is the length of the hypotenuse?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2+%2B+b%5E2++=+c%5E2
16%5E2+%2B+b%5E2+=+%282b-4%29%5E2
256+%2B+b%5E2+=+4b%5E2+-+16b+%2B+16
3b%5E2+-+16b+-240+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-16x%2B-240+=+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=%28-16%29%5E2-4%2A3%2A-240=3136.

Discriminant d=3136 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+3136+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+3136+%29%29%2F2%5C3+=+12
x%5B2%5D+=+%28-%28-16%29-sqrt%28+3136+%29%29%2F2%5C3+=+-6.66666666666667

Quadratic expression 3x%5E2%2B-16x%2B-240 can be factored:
3x%5E2%2B-16x%2B-240+=+%28x-12%29%2A%28x--6.66666666666667%29
Again, the answer is: 12, -6.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-16%2Ax%2B-240+%29

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b = x
b = 12 (Ignore the negative solution)
hyp = 20 cm