SOLUTION: Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the ma

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Question 511625: Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?
Answer by stanbon(75887) About Me  (Show Source):
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Suppose you want to frame a collage of pictures. You have a 9-ft strip of wood for the frame. What dimensions of the frame give you the maximum area for the collage? What is the maximum area?
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Perimeter = 2(L + W)
9 = 2(L+W)
L+W = 4.5
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L = 4.5-W
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Area = LW
Area = (4.5-W)W
A = 4.5W - W^2
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You have a quadratic with a = -1 and b = 4.5
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Maximum area occurs when W = -b/(2a) = 4.5/(2*-1) = 2.25 ft.
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Solve for "L":
L = 4.5-W
L = 4.5-2.25 = 2.25
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Length = 2.25 ft
Width = 2.25 ft
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Max area = LW = 2.25^2 = 5.0625 sq.ft.
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Cheers,
Stan H.
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