A farmer wishes to enclose a rectangular plot using 320 meters of fencing material. one side of the land borders a river and does not need fencing. What is the largest area that can be enclosed?

Largest area that can be enclosed is 12800 m²

Explanation:

Let L be the length and W be the width.

We have only 2 sides are fenced

Fencing = 2L + W

Fencing = 320 m

2L + W = 320

W = 320 - 2L

We need to find what is the largest area that can be enclosed.

Area = Length x Width

A = LW

A = L x (320-2L) = 320 L - 2L²

For maximum area differential is zero

So we have

dA = 0

320 - 4 L = 0

L = 80 m

W = 320 - 2 x 80 = 160 m

Area = 160 x 80 = 12800 m²

Largest area that can be enclosed is 12800 m²