Solution:
Given:
The perimeter of the fencing is 400 feet.
Each plot is assumed to be a rectangle.
The three adjacent plots are as sketched below;
The perimeter of the 3plots is given by the addition of all the sides;
Hence,

Hence,

The area of a rectangle is given by;

Substituting the breadth in equation (1) into the formula for area,

To get the maximum area, we differentiate the area with respect to l and equate to zero to find the critical points.

Thus,

Since the second derivative is a negative, then the first derivative = 0 guarantees a maximum.
Also, the coefficient of l-square is negative, this also guarantees a maximum point.


Hence, the dimensions needed to get a maximum area for the plots will be;
