SOLUTION: A rectangular room must have a perimeter of 20 feet and an area of at least 20 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a f

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Question 1062061: A rectangular room must have a perimeter of 20 feet and an area of at least 20 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a foot
Answer by Alan3354(69443) About Me  (Show Source):
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A rectangular room must have a perimeter of 20 feet and an area of at least 20 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a foot
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L + W = 10 --> W = 10 - L
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L*W >= 20
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Solve L*W = 20
L*(10 - L) = 20
-L^2 + 10L - 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B10x%2B-20+=+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=%2810%29%5E2-4%2A-1%2A-20=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+20+%29%29%2F2%5C-1+=+2.76393202250021
x%5B2%5D+=+%28-%2810%29-sqrt%28+20+%29%29%2F2%5C-1+=+7.23606797749979

Quadratic expression -1x%5E2%2B10x%2B-20 can be factored:
-1x%5E2%2B10x%2B-20+=+%28x-2.76393202250021%29%2A%28x-7.23606797749979%29
Again, the answer is: 2.76393202250021, 7.23606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B10%2Ax%2B-20+%29

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L =~ 2.8 feet
W =~ 7.2 feet
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Neither L nor W can be less than 2.8 feet (to the nearest 10th)