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11 June, 14:18

Catarina and Tom want to buy a rug for a room that is 9 by 19 feet. They want to leave an even strip of flooring uncovered around the edges of the room. How wide a strip will they have if they buy a rug with an area of 119 square feet?

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  1. 11 June, 14:41
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    17ft wide

    Step-by-step explanation:

    The room is 9 by 19ft

    Length (x) = 19ft

    Width (y) = 9ft

    Area of the rug = 119ft^2

    x*y = 119 ... (1)

    For the second equation we will make sure the strip around the room is uniform in size

    9 - x = 19 - y

    -x = 19 - 9 - y

    -x = 10 - y

    x = y - 10 ... (2)

    Put the value x in equation 1

    (y - 10) y = 119

    y^2 - 10y = 119

    y^2 - 10y - 119 = 0

    a = 1, b = - 10, c = - 119

    Use quadratic formula to solve the equation

    y = (-b + / -√b^2 - 4ac) / 2a

    y = [ - (-10) + / - √ (-10) ^2 - 4 (1) (-119) ] / 2 (1)

    y = (10 + / - √100 + 476) / 2

    y = (10+/-√ 576) / 2

    y = (10 + / - 24) / 2

    y = (10 + 24) / 2 or (10 - 24) / 2

    y = 34/2 or - 14/2

    y = 17 or - 7

    y = 17 ft

    Recall that x = y - 10

    x = 17 - 10

    x = 7ft
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