if the farmer wants 3 equal rectangular pens,then each pen would be made by 200 ft of fence.suppose that the length connect to the barn is x ft,then the other sides of the rectangle have the identical length of (200-x)/2 ft.hence the pen area is S=x(200-x)/2,when x=100ft S has the maximum value that is 5000 sqrft
the length of each side are 100ft 50ft 50ft