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27 November, 15:21

Joan wants to buy a rug for a room that is 1111 feet by 1414 feet. she wants to leave a uniform strip of floor around the rug. she can afford 8888 square feet of carpeting. what dimensions should the rug have?

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  1. 27 November, 18:28
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    Solution:

    Let x be the width of the strip.

    Width of rug = 1111 - 2x

    Length of rug = 1414 - 2x

    Area of carpet = 8888

    Area = Length * Width

    8888 = (1414 - 2x) (1111 - 2x)

    8888 = 1570954 - 2222x - 2828x + 4x²

    4x² - 5050x + 1562066 = 0

    2x² - 2525x + 781033 = 0

    x = 720.5, 542

    So, the value of x is 542.

    Width of rug = 1111 - 2 (542) = 27

    Length of rug = 1414 - 2 (542) = 330

    Hence, the dimensions are 330, 27.
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