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March 25, 2017

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A gardener wants to fence in her plot in two equal rectangular sections. If she has 120 yards of fence and the area of the entire plot is 384 yd 2, find the possible dimensions in yards of the garden.

  • College Algebra - ,

    Eq1: L*W = 384yds^2.
    @l + 2W = 120
    Divide both sides by 2:
    L + W = 60.

    Eq1: L * W = 384.
    Eq2: L + W = 60.
    Solve for L in Eq2:
    L = 60 - W.
    In Eq1, substitute 60-W for L:
    (60-W)W = 384
    -W^2 + 60W -384 = 0.
    Solve using Quadratic Formula and get:
    W = 7.28 or 52.7.
    Substitute 7.28 for W in Eq1:
    7.28*L = 384
    L = 52.7 Yds.

    Solution:
    L = 52.7 Yds.
    W = 7.28 Yds.

    To form 2 equal rectangular sections:
    L = 52.7 Yds.
    W = 7.28/2 = 3.64 Yds.
    OR
    L = 52.7 / 2 = 26.35 Yds.
    W = 7.28 Yds.

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