A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 3 identical smaller rectangular plots by placing two fences parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area.
|||Length of shorter side: x
Length of longer side: y
We know that:
2y+4x=800
A=y*x=(400-2x)*x=400x-2x^2
To find the maximum:
A'=400-4x=0
x=100
y=400-2x=200|||2x+4(x/2)=800
so the two long sides would equal 100 and the two shorter sides would equal 100. Then the two dividing fences in between to give three smaler rectangular plots would also equal 100. So you have four 100 sides and two 200 sides which equals 800
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