The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.

    P = 2l + 2w
    Since P = 120, we have:
    (1) 2l + 2w = 120

    We are also given:
    (2) l = 3w - 6

    Substitute equation (2) into equation (1)
    2(3w - 6) + 2w = 120

    Multiply through:
    6w - 12 + 2w = 120

    Combine like terms:
    8w - 12 = 120

    Add 12 to each side:
    8w = 132

    Divide each side by 8 to isolate w:
    w =16.5

    Now substitute w into equation (2)
    l = 3(16.5) - 6
    l = 49.5 - 6
    l = 43.5

    So (l, w) = (43.5, 16.5)


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