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19 April, 15:38

The width of rectangle A is the sum of twice a number and 8. The length of the rectangle is 3 times as great as the width. If the perimeter is 96 feet, find the length and width.

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  1. 19 April, 17:11
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    Formula for perimeter of a rectangle = 2 (L + W)

    let the number be x

    width = 2x + 8

    length = 3 (2x + 8)

    substitute respectively

    96 = 2 (2x + 8 + 3 (2x + 8)) open the bracket

    96 = 2 (2x + 8 + 6x + 24) collect like terms

    96 = 2 (8x + 32) open the bracket

    96 = 16x + 64

    collect like terms

    96 - 64 = 16x

    32 = 16x

    divide both sides by 16

    32/16 = 16x/16

    2 = x

    therefore, the width = 2x + 8 = 2 (2) + 8 = 4 + 8 = 12.

    and the length = 3 (2x + 8) = 6x + 24 = 6 (2) + 24 = 12 + 24 = 36.
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