# math

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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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