SOLUTION: The length of a rectangular lawn is 5 feet more thanits width. If the area of the lawn is 980 square feet, find the dimensions of the lawn. Round to the nearest tenth of a foot.

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Question 1104020: The length of a rectangular lawn is 5 feet more thanits width. If the area of the lawn is 980 square feet, find the dimensions of the lawn. Round to the nearest tenth of a foot.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular lawn is 5 feet more thanits width. If the area of the lawn is 980 square feet, find the dimensions of the lawn. Round to the nearest tenth of a foot.
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L = W + 5
L*W = 980
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W*(W+5) = 980
W^2 + 5W - 980 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-980+=+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=%285%29%5E2-4%2A1%2A-980=3945.

Discriminant d=3945 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+3945+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+3945+%29%29%2F2%5C1+=+28.9046174948844
x%5B2%5D+=+%28-%285%29-sqrt%28+3945+%29%29%2F2%5C1+=+-33.9046174948844

Quadratic expression 1x%5E2%2B5x%2B-980 can be factored:
1x%5E2%2B5x%2B-980+=+%28x-28.9046174948844%29%2A%28x--33.9046174948844%29
Again, the answer is: 28.9046174948844, -33.9046174948844. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-980+%29

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W = 28.9