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3 April, 08:34

Pool measuring 10 ft by 20 feet will have a cement walkway around it. The area covered by the pool and the cement walkway is 600 square feet. If the walkway must have a uniform width around the entire pool, what is the width of the walkway?

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  1. 3 April, 11:31
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    Answer:the width of the walkway is 5 feet

    Step-by-step explanation:

    Let x represent the width of the walkway.

    The pool measures 10 ft by 20. If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway would be 10 + x + x = 10 + 2x

    The total width of the pool and the walkway would be 20 + x + x = 10 + 2x

    The area covered by the pool and the cement walkway is 600 square feet. This means that

    (10 + 2x) (20 + 2x) = 600

    200 + 20x + 40x + 4x^2 = 600

    4x^2 + 60x + 200 - 600 = 0

    4x^2 + 60x - 400 = 0

    Dividing through by 4, it becomes

    x^2 + 15x - 100 = 0

    x^2 + 20x - 5x - 100 = 0

    x (x + 20) - 5 (x + 20) = 0

    (x - 5) (x + 20) = 0

    x = 5 or x = - 20

    The width cannot be negative. Therefore, the width of the walkway is 5 feet
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