Arectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric fence. with 19001900 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

Let x denote the length of the side of the garden which is bounded by a river, then other (adjacent) side of the farmland has a measure of .

The perimeter of a rectangle is given by 2(length + width).

Given that one of the sides is to be bounded by a river, the the perimeter of the remaining three sides to be fenced is given by


Given that there is 1,900 m of wire available to bound the three sides, then the perimeter of the three sides is equal to 1,900

Thus


For the area to be maximum, the differentiation of A with respect to x must be equal to 0.
i.e.


Therefore, the maximum area of the garden enclosed is given by


The dimensions of the farmland is 950m by 451,250 / 950 = 950m by 475m