SOLUTION: if the hypotenuse of a right triangle is 52 in. one leg of the triangle is 8 in more than twice the length of the other. what is the perimeter of the triangle?

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Question 806389: if the hypotenuse of a right triangle is 52 in. one leg of the triangle is 8 in more than twice the length of the other. what is the perimeter of the triangle?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
c=52, a=2b+8
a^2+b^2=c^2
(2b+8)^2+b^2=52^2
4b^2+32b+64+b^2=2704
5b^2+32b-2640=0 see below
b=20, a=48
48+20+52
=120"
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B32x%2B-2640+=+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=%2832%29%5E2-4%2A5%2A-2640=53824.

Discriminant d=53824 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+53824+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+53824+%29%29%2F2%5C5+=+20
x%5B2%5D+=+%28-%2832%29-sqrt%28+53824+%29%29%2F2%5C5+=+-26.4

Quadratic expression 5x%5E2%2B32x%2B-2640 can be factored:
5x%5E2%2B32x%2B-2640+=+5%28x-20%29%2A%28x--26.4%29
Again, the answer is: 20, -26.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B32%2Ax%2B-2640+%29