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A farmer has 80 feet of fencing, which she plans to use to fence in a plot of land for a pigpen. If she chooses to enclose a plot along the broad side of her barn, what is the largest area that can be enclosed? (Note: The side along the barn will not require fencing)

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Chelsea

  1. let the width of the field be x ft
    let the length be y ft
    so y + 2x = 80
    or y = -2x + 80

    area = xy
    = x(-2x+80)
    = -2x^2 + 80x

    do you know Calculus?
    if so ...
    d(area)/dx = -4x + 80 = 0 for a max area
    4x = 80
    x = 20
    width is 20 ft, length is 40 ft.
    largest area = 20(40) = 800 ft^2

    If you don't know Calculus, complete the square

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    Reiny

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