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) (Show Source): You can put this solution on YOUR website!
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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