A rectangular field is to be enclosed by a fence and divided into two smaller plots by a fence parallel to one of the side. Find the dimensions of the largest such field if 1200 m of fencing material is available. What is the area of this field and what are the dimensions that will give the largest area?

Answer 1

Draw a diagram. There will be 3 strips of one length, and 2 strips of the other. If we call them x and y, then
3x+2y=1200
The area is
A = xy=x(1200-3x)/2 = 600x-3/2 x^2
The maximum area occurs at the vertex of the parabola, at
x = -b/2a = 200

So, there will be 3 lengths of 200
and 2 lengths of 300
The maximum area is 60,000 m^2

As with all such problems, the maximum area is achieved when the fencing is divided equally between lengths and widths, no matter how many of each there are.

In this case, 1200/2 = 600
since there are 3 lengths (x), each is 200
There are 2 widths (y), each is 300