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a rectangular garden is to be fenced along four sides and in the middle it is to be divided into 2 equal areas.if 300meters of fencing materials is available, find the maximum possible area that can be fenced.

  • math -

    make a sketch, so you will have 2 longs sides and 3 short sides parallel with the divider.
    Let the long sides by y, and the short sides be x
    3x + 2y = 300
    y = (300 - 3x)/2 = 150 - 1.5x
    Area = xy
    = x(150-1.5x)
    = 150x - 1.5x^2
    = -1.5(x^2 - 100x + 2500 - 2500)
    = -1.5(x-50)^2 + 3750

    Max area = 3750 m^2

    check: x = 50, y = 75
    area = 3750, 3x+2y= 150+150 = 300

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