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)   (Show Source): You can put this solution on YOUR website!
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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.76393202250021, 7.23606797749979. Here's your graph:

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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)

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