SOLUTION: find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.

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Question 637860: find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the dimensions of a rectangular garden that has a perimeter 100 ft and area 300 ft squared.
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P = 2L + 2W = 100
L + W = 50
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L*W = 300
L*(50-L) = 300
L^2 - 50L + 300 = 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-50x%2B300+=+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=%28-50%29%5E2-4%2A1%2A300=1300.

Discriminant d=1300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+1300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+1300+%29%29%2F2%5C1+=+43.0277563773199
x%5B2%5D+=+%28-%28-50%29-sqrt%28+1300+%29%29%2F2%5C1+=+6.97224362268005

Quadratic expression 1x%5E2%2B-50x%2B300 can be factored:
1x%5E2%2B-50x%2B300+=+%28x-43.0277563773199%29%2A%28x-6.97224362268005%29
Again, the answer is: 43.0277563773199, 6.97224362268005. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-50%2Ax%2B300+%29

L = x
L = 25 + 5sqrt(13) ft
W = 25 - 5sqrt(13) ft