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For the city park commission, you are designing a marble planter in which to plant flowers. You want the length of the planter to be six times the height and the width of to be three times the height. The sides should be one foot thick. Since the planter will be on the sidewalk, it does not need a bottom. What should the outer dimentions of the planter be if it is to hold 4 cubic feet of dirt?

  • math -

    L = 6 h
    W = 3 h

    (L-2)(W-2)h = 4
    (6h-2)(3h-2)h = 4
    (18 h^2 - 18 h +4)h = 4
    18 h^3 - 18 h^2 + 4 h - 4 = 0
    That happens to be zero when h = 1, so that is a solution
    If h = 1
    L = 6
    W = 3

    That answers the question, but check to see if there are other solutions
    dividing by (h-1)
    I get
    18 h^2 + 4 = 0
    that has imaginary solution, so h = 1 is the only real solution.

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