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March 30, 2017

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Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 160 feet. Find the value(s) for which the area is 2800 square feet.

  • PreCalculus - ,

    Let the length of the side parallel to the wall be x. The two perpendicular sides will then each be y in length.

    Solve this pair of equations:
    x + 2y = 160
    x y = 2800

    (160-2y)y = 2800
    -2y^2 +160y = 2800
    y^2 -80y +1400 = 0

    Solve for y or factor. It looks to me like the answer is not an integer, there may be two solutions. Use the quadratic equation.

    y = [80 + sqrt(800)]/2

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