pre calculus min/max area/perimeter

Question

a farmer wants to build three rectangular pens of the same size next to a river so that they are separated by two fences. If she has 1,000 feet of fencing and does not fence the side next to the river, what are the dimensions of the largest area she can enclose

Answer 1

1000 feet of fencing to enclose 3 rectangular pens

one side with a river, so no fencing needed there

what is maximum area possible??

let x = side parallel to the river

y = each of 4 perpendicular sides = (1000-x)/4

Area = XY = x(1000-x)/4 = 250x - (x^2)/4

A' = 250 -x/2 = 0

x =500

y = 500/4 = 125

max Area = XY = 125(500) = 62500 square feet