SOLUTION: the perimeter of a rectangle is 88cm. Find the maximum area possible for a rectangle with this perimeter.

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Question 165099: the perimeter of a rectangle is 88cm. Find the maximum area possible for a rectangle with this perimeter.
Answer by Alan3354(69443) About Me  (Show Source):
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the perimeter of a rectangle is 88cm. Find the maximum area possible for a rectangle with this perimeter.
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L = Length
W = Width
perimeter = 2L + 2W = 88
Area =L*W
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2L + 2W = 88
L+W = 44
L = 44-W
Substitute into eqn for Area
A = (44-W)*W
88 = 44W - W^2
W^2 - 44W + 88 = 0
Set the 1st derivative = 0
2W - 44 = 0
W = 22
Maximum area (for a rectangle) is a square.
Each side is 22 cm
The area is 22x22 = 484 sq cm