Question 169542: The perimeter of a rectangle window is 32 ft. Find the dimensions of the window that will enclose the largest area. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! The perimeter of a rectangle window is 32 ft. Find the dimensions of the window that will enclose the largest area.
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Let W = width
and L = length
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Since perimeter is:
2(L + W) = 32
L + W = 16
L = 16-W
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Area = W(16-W)
Area = -W^2 + 16W
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By inspection, we see (from the -1 coefficient associated with W^2) that it is a parabola which opens downward -- therefore, the "axis of symmetry" should give you the max.
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Axis of symmetry:
W = -b/2a
W = -16/2(-1)
W = 8 feet (width)
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Length:
16-W = 16-8 = 8 feet (length)
