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March 25, 2017

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A rectangular field is to be enclosed by a fence and divided into three equal rectangular parts by two other fences. find the maximum area that can be enclosed and separated in this way with 1200m of fencing.

  • precalculus - ,

    let the width of the whole rectangle be x m (there will be 4 of these)
    let the length be y m
    then 4x + 2y = 1200
    2x + y = 600
    y = 600 - 2x

    Area = xy
    = x(600-2x)
    = -2x^2 + 600x

    Now, I don't know if you are studying Calculus.
    If you do, then
    d(Area)/dx = -4x + 600
    = 0 for a max area
    x = 150

    then y = 600 - 2(150) = 300
    and the max area is (150)(300) = 45000

    If you don't know Calculus, complete the square on the above quadratic
    you should end up with
    Area = -2(x-150)^2 + 45000

  • precalculus - ,

    45000

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