rectangular area question?

Question

a man wishes to put a fence around a rectangular field and then subdivided the field into 3 smaller rectangular plots by placing two fences parallel to one of the sides. If he can afford only 2000 yards of fencing, what dimensions will give him the maximum rectangular area?

Answer 1

x= one of the 3 parallel segments

2000-3x left to divide equally for the other two sides

x/2(2000-3x) =-3/2 x^2 +1000x

this is an inverted parabola and the vertex of the graph will give the maximum x.

-b/2a =-1000 / 2(-3/2) =1000/3 yards for each of the three parallel sides

leaving 500 yards each for the other two sides

500(1000/3) =500000/3 sq yds is the max area