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16 October, 17:20

A pool measuring 16 meters by 22 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 832 square meters, what is the width of the path?

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  1. 16 October, 19:44
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    Let X be the width of the path.

    The width of the path would be the width of the pool plus 2x, so 2x + 16

    The length of the path would be the length of the pool plus 2x, so 2x+22

    The total area is 832 square feet.

    Area is found by multiplying the length by the width.

    So you have:

    (2x+16) (2x+22) = 832

    Use the Foil Method:

    (2x+16) (2x+22) = 4x^2 + 76x+352

    Now you have:

    4x^2 + 76x+352 = 832

    Subtract 832 from both sides:

    4x^2 + 76x+352-832 = 0

    Simplify:

    4x^2 + 76x - 480

    Factor the left side:

    4 (x-5) (x+24) = 0

    Divide both sides by 4:

    (x-5) (x+24) = 0

    Set both parenthesis to equal 0 and solve for x:

    x=5 and x = - 24

    The width of the path cannot be a negative number, so the width is 5 meters.
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