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8 February, 03:13

Among all the rectangles whose perimeters are 100 feet, find the dimensions of the one with the maximum area. explain step by step.

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  1. 8 February, 03:23
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    We let x be the length and y be the width of the rectangle. Then,

    Perimeter = 2x + 2y

    100 = 2x + 2y

    50 = x + y

    y = 50 - x

    Area = xy

    A = x (50 - x)

    A = 50x - x^2

    We then take the derivative; set it equal to zero:

    A ' = 50 - 2x

    0 = 50 - 2x

    2x = 50

    x = 25

    y = 50 - x

    y = 50 - 25

    y = 25

    Therefore, the dimensions are 25 and 25.
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