A farmer has 576m of fencing to create a rectangular pasture divided into three separate pastures all with the same dimensions. What is the maximum area that the farmer can have fenced?
+129840 We have an expression for the total perimeter of fencing
6W + 4L = 576 where W is the width of each pasture and L is the length
So....simplifying
2L = 288 - 3W → L = 144 - 1.5W
And the total area is
A = 3W * L = 3W [ 144 - 1.5W ] = 432W - 4.5W^2
Take the derivative of the area and set to 0
432 - 9W = 0
9W = 432
W = 48 ft
And L = 144 - 1.5 (48) = 144 - 72 = 72 ft
So...the max area = 3(48)* (72) = 10,368 ft^2
