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10 April, 09:28

Bob has 60 feet of fencing, which he intends to use to enclose a rectangular garden. If the length of the garden is x feet long, he wants the width to be (40-2x) feet wide. What value of x will result in the largest area for the garden?

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  1. 10 April, 09:41
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    x = 10 feet.

    Perimeter of a rectangle = 2 (l + w)

    Area of a rectangle = w*l

    P = 60ft

    Length = x

    Width = 40-2x

    A = ?

    60 = 2 (x + (40-2x)

    60 = 2x + 80 - 4x

    60 = - 2x + 80

    2x = 80 - 60

    2x = 20

    2x / 2 = 20 / 2

    x = 10 - - length

    Width = 40 - 2x; where x = 10; 40 - 2 (10) = 40 - 20 = 20.

    P = 2 (l + w)

    60 = 2 (10 + 20)

    60 = 2 (30)

    60 = 60

    Area = w * l

    A = 20 * 10

    A = 200 square feet
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