A rectangular 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 1100 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions?

Length = 550 m

Width = 275 m

Area = 151,250 m2

Step-by-step explanation:

One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:

And the area of the farmland is given by:

From the Perimeter equation, we have that:

Using this in the area equation, we have:

Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:

This width will give the maximum area of the farmland. Now, finding the length and the maximum area:

a. is correct