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21 August, 09:49

A gift box's rectangular base has a perimeter of 92 centimeters. The length of the base is one more than twice the base's width. Find the width (in centimeters) of this rectangular base.

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  1. 21 August, 10:26
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    Assume that the length of the rectangle is "l" and that the width is "w".

    We are given that:

    (1) The length is one more than twice the base. This means that:

    l = 2w + 1 ... > equation I

    (2) The perimeter is 92 cm. This means that:

    92 = 2 (l+w) ... > equation II

    Substitute with equation I in equation II to get the width as follows:

    92 = 2 (l+w)

    92 = 2 (2w+1+w)

    92/2 = 3w + 1

    46 = 3w + 1

    3w = 46-1 = 45

    w = 45/3

    w = 15

    Substitute with w in equation I to get the length as follows:

    l = 2w + 1

    l = 2 (15) + 1

    l = 30 + 1 = 31

    Based on the above calculations:

    length of base = 31 cm

    width of base = 15 cm
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