Question

A farmer has 1792 feet of fencing available to endose a rectangular area bordering a river. If no fencing is required along the river find the dimensions of the fencedarea that will maximize the area. What is the maximum area?What is the length of the fenced area?

Answer 1

Area is length * width

We want to maximize the area.

We also know he has to cover 3 sides with 1792 feet of fencing.

Let one length (side) be the river, so we have:

2 width sides

1 length sides

Thus, we can write:

2w + l = 1792

or

l = 1792 - 2w

Area = l * w

Substituting, we get: