# Build a rectangular pen with three parallel partitions (meaning 4 total sections) using 500 feet of fencing. What dimensions will maximize the total area of the pen?

##### 1 Answer

The dimensions that will maximize the area the total area of the pen will be

Total area with these dimensions:

#### Explanation:

Step 1: Set up a picture/diagram to help answer the question and write out the needed equations.

Diagram:

The total length will be

Needed Equations:

Perimeter of this diagram

Total Area

Step 2: Solve for

Step 3: Substitute the equation for

Step 4: Find the derivative of the equation for area.

Step 5: Use the derivative equation in order to find the critical point(s) that maximize the area.

Critical points are when

Since

Step 6: Find the height (

The dimensions that will maximize the area the total area of the pen will be

Step 7: Find the total area of the pen.