# A farmer owns 1000 meters of fence, and wants to enclose the largest possible rectangular area. The region to be fenced has a straight canal on one side, and thus needs to be fenced on only three sides. What is the largest area she can enclose?

##### 1 Answer

Jun 20, 2015

I found:

#### Explanation:

Considering the field as:

I know that the perimiter (only on 3 sides) to be fenced is equal to the meters of fence at disposal of the farmer:

The area will be

From (1)

Derive

equal it to zero to maximize it:

use this back in (1) you find

Use these dimensions in (2):