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A dog trainer has 64 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 192 ft2, what will be the dimensions of the work area?

  • Algebra -

    guessing way:
    192 = 2^6*3 = 16*12 = 8*24
    2(8+24) = 64
    so the work area is 8x24

    algebraic way:
    If the pen's width is w, then the length is 32-w

    w(32-w) = 192
    w^2 - 32w + 192 = 0
    (w-8)(w-24) = 0
    w = 8 or 24
    so, the pen is 8x24

    Unless you use the quadratic formula, factoring the polynomial is essentially the same as guessing the right factors of 192!

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