9514 1404 393
Answer:
26.25 ft by 21 ft
Step-by-step explanation:
Let x represent the length of the set of pens along the side of the building. Then the fence remaining for the 5 partitions out from the building (2 ends + 3 partitions, all the same length) will be (210-x). Since each of those partitions is (210-x)/5, the overall area will be ...
A(x) = x(210-x)/5
This describes a downward-opening parabola with zeros at x=0 and x=210. The maximum area is on the line of symmetry, halfway between those zeros. The area is a maximum when x=210/2 = 105.
The horizontal dimension of each pen is (105 ft)/4 = 26.25 ft.
The dimension out from the building is (210 -105 ft)/5 = 21 ft.
The dimensions of each pen should be 26.25 feet wide and 21 feet out from the building.
