The dimensions of each pen will maximize the total enclosed area are: Length 81 feet; Width 81 feet.
Dimension of each pen
Length = x
Width = y
Area = xy
Perimeter equation is
2(x + y) = 324
x + y = 162
Substituting the perimeter equation
Area = x(162 - x)
Area = -x2 + 162x
If the zeros of the quadratic are 0 and 162, then the median will be where the maximum area occurs.
162/ 2
= 81
Hence, the dimensions are
Length = 81 feet
Width = 162 - 81 = 81 feet
Therefore the dimensions of each pen will maximize the total enclosed area are: Length 81 feet; Width 81 feet.
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