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The perimeter of a paved area being built at a playground is going to be 46 meters. If the length and width are each a whole number of meters, what should the length and width of the area be to cover the greatest possible area?

  • math -

    let the length be x
    and the width be y
    2x + 2y = 46
    x+y = 23
    y = 23 - x

    area = xy
    = x(23-x) = -x^2 + 23x

    vertex of this parabola :
    the x of the vertex is -b/(2a) = -23/-2 = 11.5
    then y = 23-11.5 = 11.5

    So the paved area should be a square with sides 11.5 m each , resulting in a maximum area of 132.25 m^2

    (Of course , the largest rectangle for a given perimeter is always a square)

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