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5 August, 06:46

The length of a rectangular table is 1 foot more than twice the length of a side of a square rug and the width of the table is 3 feet less than the length of a side of the rug. if the area of the table is 81 ft squared greater than the area of the rug, what is the area of the rug?

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  1. 5 August, 09:41
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    Let us assume the length of a side of a square rug = x

    Then

    Length of the rectangular table = (2x + 1) feet

    Width of the rectangular table = (x - 3) feet

    Area of the square rug = (Side) ^2

    = x^2

    Area of the rectangular table = (x^2 + 81) square feet

    Now

    Area of the rectangular table = Length * Width

    x^2 + 81 = (2x + 1) * (x - 3)

    x^2 + 81 = 2x^2 - 6x + x - 3

    x^2 + 81 = 2x^2 - 5x - 3

    2x^2 - x^2 - 5x = 81 + 3

    x^2 - 5x = 84

    x^2 - 5x - 84 = 0

    Now we can solve this equation by factoring method and we will get

    (x + 7) (x - 12) = 0

    As x cannot be negative. so

    x - 12 = 0

    x = 12

    Then

    Area of the rug = x^2

    = (12) ^2

    = 144 square feet

    So the area of the rug is 144 square feet.
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