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algebra 2

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Minnie and Steve have arectangular swimming pool that is 12 ft. wide and 20 feet long. They are going to build a tile border of uniform width around the pool. They have 160 sq. ft. of tile. How wide should the border be?

  • algebra 2 -

    area of pool only = 12x20 = 240 ft^2

    let the width of the border be x ft
    so area of pool + border
    = (12+2x)(20+2x) = 4x^2 + 64x + 240

    New area - pool area = tile area
    4x^2 + 64x + 240 - 240 = 160
    4x^2 + 64x - 160 = 0
    x^2 + 16x - 40 = 0

    complete the square
    x^2 + 16x + 64 = 40 + 64
    (x+8)^2 = 104
    x+8 = √104
    x = ±√104 - 8
    x = appr 2.2 ft or a negative, which would be silly

    the border should be 2.2 ft wide

    (good luck finding a 2.2 ft tile, looks like a lot of wasteful cutting)

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