Math

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A rectangular study area is to be enclosed by a fence and divided into two equal parts, with a fence running along the division parallel to one of the sides. if the total area is 384 ft^2, find the dimensions of the study area that will minimize the total length of the fence. How much fence will be required?

  • Math -

    p = perimeter = 3 L + 2 B

    384 = L B so B = 384/L

    p = 3 L + 768/L
    dp/dL = 3 - 786 /L^2
    = 0 for minimum
    3 L^2 = 786
    L^2 = 256
    L = 16
    B = 384/16 = 24
    B/2 = 12
    so two 12 by 16 areas

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