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The length of a rectangle is 5ft longer than twice the width. If the perimeter is 106ft, find the length and the width of the rectangle.

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asked by Amber
  1. P = 2L + 2W

    106 = 2(W + 5) + 2W

    106 = 4W + 10

    96 = 4W

    24 = width

  2. What we know:

    Length = 2X + 5
    Width = X

    Perimeter = 2L + 2W
    106 = 2(2X + 5) + 2X
    106 = 4X + 10 + 2X
    106 - 10 = 6X
    96 = 6X

    96 = 6X
    ___ ___
    6 6

    16 = X

    Now we know X is 16 (Width)

    Let's substitute:

    Width = 16
    Length = 2X + 5
    = 2(16) + 5
    = 37

    Double check answers:

    Perimeter = 2L + 2W
    106 = 2(37) + 2(16)
    106 = 74 + 32

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