posted by Ashlee

You want to build a garden around your garden. One side borders your house so it does not need a fence. If you only have 50m of fencing what dimensions should you make your garden in order to maximize the area?

  1. Reiny

    Let the side parallel to the house by y
    the each of the other two sides be x
    Make a sketch

    2x + y = 50
    y = 50-2x

    area = xy
    = x(50-2x)
    =50x - 2x^2

    the x of the vertex of this parabola is -b/(2a) = -50/-4 = 12.5

    so x = 12.5
    and y = 50-25 = 25

    The garden should be 25 m long and 12.5 m wide

    by Calculus:
    area = 50x - 2x^2
    d(area)/dx = 50-4x = 0 for a max of area
    x = 12.5
    continue as above

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