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17 September, 00:56

Of all rectangles with a perimeter of 29, which one has the maximum area? (Give the dimensions) The rectangle that has the maximum area has length ___ and width __.

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  1. 17 September, 03:50
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    Both length and width of 7.25m

    Step-by-step explanation:

    Let L and W be the length and width of the rectangle, respectively. Since the perimeter is 29, we have the following equation

    (L + W) 2 = 29

    L + W = 29/2 = 14.5

    L = 14.5 - W

    Also the area of the rectangle would be as the following:

    A = LW = W (14.5 - W) = 14.5W - W^2

    To find the maximum area possible, we can take the first derivative and set it to 0

    A' = 14.5 - 2W = 0

    2W = 14.5

    W = 14.5 / 2 = 7.25m

    L = 14.5 - W = 14.5 - 7.25 = 7.25m
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