math 099

a rancher wants to use 300 feet of fencing to enclose a rectangular area of 4400 square feet. what dimensions should the rectangle have?

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  1. length = x
    width = y

    x+y = 150 , y = 150-x

    xy = 4400
    x(150-x) = 4400
    expanding and simplifying...
    x^2 - 150x + 4400 = 0
    (x-110)(x-40) = 0
    x = 110 or x=40

    if x=110, then y = 40
    if x = 40, then y = 110

    the dimenstions should be 110 ft by 40 ft

    check: 2(110+40) = 300
    (110)(40) = 4400

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