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1 October, 12:07

What is the largest rectangular area that can be enclosed with 400 feet of fencing?

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  1. 1 October, 15:59
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    Let the length = x

    2 lengths are 2x.

    Then you have 400 - 2x for both widths, so the width is 200 - x.

    The are if the rectangle is

    y = x (200 - x)

    y = 200x - x^2

    y = - x^2 + 200x

    Take the first derivative ans set equal to zero to find a maximum value.

    y' = - 2x + 200

    -2x + 200 = 0

    -2x = - 200

    x = 100

    Since the side of the rectangle is 100, all sides measure 100 ft, and you have a square.

    The maximum area is 100 ft * 100 ft = 10,000 ft.
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