SOLUTION: You have 164 feet of fencing to enclose a rectangular region. Write an area equation in terms of width w . Find the dimensions of the rectangle that maximizes the enclosed area.

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Question 1058725: You have 164 feet of fencing to enclose a rectangular region. Write an area equation in terms of width w . Find the dimensions of the rectangle that maximizes the enclosed area.
Answer by ikleyn(52797) About Me  (Show Source):
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You have 164 feet of fencing to enclose a rectangular region. Write an area equation in terms of width w.
Find the dimensions of the rectangle that maximizes the enclosed area.
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If the width is "w", then the length is 164%2F2+-+w = 82 - w,
and the area is A = (82-w)*w.

A rectangle having the maximal area at given perimeter is a square with the side equal to 1%2F4 of the perimeter.
164%2F4 = 41 feet in this case.


See the lessons
    - A rectangle with a given perimeter which has the maximal area is a square
    - A farmer planning to fence a rectangular garden to enclose the maximal area
in this site.