Algebra

Farmer Ed has
9,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

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  1. x = length
    y = width

    x + 2 y = 9000 or x = 9000 - 2 y
    A = x y
    so
    A = (9000-2y)y

    2 y^2 - 9000 y = - A
    y^2 - 4500 y = -A/2

    y^2 - 4500 y +(4500/2)^2 = -A/2 + 5,062,500

    (y-2250)^2 = -(1/2)(A-10,125,000)
    so
    width = 2250
    length = 4500
    area = 10,125,000 m^2

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