SOLUTION: The perimeter of a rectangle is 800m and the are is 80m square .find the length of the rectangle

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Question 1105757: The perimeter of a rectangle is 800m and the are is 80m square .find the length of the rectangle
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of a rectangle is 800m and the are is 80m square .find the length of the rectangle
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2L + 2W = 800
L + w = 400 --> L = 400 - W
L*W = 80
Sub for L
W*(400-W) = 80
w^2 - 400W + 80 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-400x%2B80+=+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=%28-400%29%5E2-4%2A1%2A80=159680.

Discriminant d=159680 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--400%2B-sqrt%28+159680+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-400%29%2Bsqrt%28+159680+%29%29%2F2%5C1+=+399.799899899875
x%5B2%5D+=+%28-%28-400%29-sqrt%28+159680+%29%29%2F2%5C1+=+0.200100100125184

Quadratic expression 1x%5E2%2B-400x%2B80 can be factored:
1x%5E2%2B-400x%2B80+=+%28x-399.799899899875%29%2A%28x-0.200100100125184%29
Again, the answer is: 399.799899899875, 0.200100100125184. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-400%2Ax%2B80+%29

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W is one of the solutions, L is the other.