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29 November, 03:05

Find the length and width of a rectangle that has the given perimeter and a maximum area. perimeter: 128 meters

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  1. 29 November, 03:47
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    P = 128 meters = 2W + 2L. We want to maximize the area: A = L*W

    Solve 128 meters = 2W + 2L for either W or L:

    64 meters = W + L, so W = 64-L

    and subst. your result into

    A = L*W: A = L * (64-L). Then A (L) = 64L - L^2. You could graph this and find the approx value of L at which A (L) is at its max.

    Or, if you know calculus, differentiate A (L) and set the result = to 0. Solve for L.

    L + W = 64, so you can subst. your value for L into this eqn to find W.
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