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8 November, 02:57

A rectangular field is 4 times as long as it is wide. If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. Find the dimensions of the original field. The original dimensions are feet long by feet wide.

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  1. 8 November, 03:12
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    L = 4W [A rectangular field is 4 times as long as it is wide.]

    2 (L-10) + 2 (W+2) = 80 [If the length is decreased by 10 feet and the width is increased by 2 feet, the perimeter will be 80 feet. ]

    Distributed: (2L - 20) + (2W + 4) = 80

    Substitute the known value of L from the first equation into the second.

    8W - 20 + 2W + 4 = 80

    10 W - 16 = 80

    Add 16 to each side

    10W = 96

    Divide each side by 10

    W = 9.6 <<--original dimension

    L = 9.6 * 4 = 38.4 <<--original dimension

    ...

    If the length (38.4) is decreased by 10 feet (which would make it 28.4) and the width (9.6) is increased by 2 feet (11.6), the perimeter will be 80 feet.

    28.4 + 28.4 + 11.6 + 11.6 = 80 feet.

    Have a nice day : D
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