Question 337281: A Carpenter is building a rectangular room with a fixed perimeter of 192ft. What dimensions would yield the maximum area? What is the maximum area?
the length that would yield the maximum area is ________ ft.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A Carpenter is building a rectangular room with a fixed perimeter of 192ft.
Perimeter = 2(L + W)
192 = 2(L+W)
L + W = 96
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What dimensions would yield the maximum area? What is the maximum area?
the length that would yield the maximum area is ________ ft.
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Area = LW
A = L(96-L)
A = -L^2+96L
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Quadratic with a = -1 and b = 96
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Maximum Area occurs when L = -b/(2a) = -96/(2*-1) = 48
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If L = 48 ft. and L+W = 96, W = 48 ft.
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Maximum Area = 48*48 = 2304 sq. ft.
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Cheers,
Stan H.
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