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6 July, 05:54

Among all rectangles that have a perimeter of 210, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

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  1. 6 July, 06:38
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    Let the length of the rectangle be x units then the width = (210 - 2x) / 2

    = 105 - x units

    Area A = x (105 - x) = 105x - x^2

    Finding the derivative:_

    dA/dx = 105 - 2x = 0 for max/minm volume

    x = 52.5

    this is for a maximum area because second derivative is negative ( = - 2).

    width = 105 - 52.5 = 52.5

    Dimension for maximum area = 52 1/2 * 52 1/2. (The rectangle is actually a square).
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