Math

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A farmer has 36 feet of fence to build a pigpen. He is going to use one of the sides of his barn as a side to the rectangular enclosure. Determine a function A that represents the total area of the enclosed region. What is the maximum area that can be enclosed?

  • Math -

    A = L * w
    Perimeter = L + 2 w = 36
    so
    L = 36-2w

    A = (36-2w)w

    -2 w^2 + 36 w = A

    w^2 - 18 w = -A/2

    w^2 - 18 w + 81 = -A/2 + 81

    (w-9)^2 = -(1/2)(A-162)

    vertex at
    w = 9
    area = 162 ft^2
    ====================
    check
    if w = 9
    L = 36 - 18 = 18
    area = 162, sure enough

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