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Example 1

A farmer is building a rectangular pen using feet of electric fencing and the side of a barn. In addition to fencing, there will be a -foot gate also requiring the electric fencing on either side of the pen. The farmer wants to maximize the area of the pen. How long should he make each side of the fence in order to create the maximum area?
  1. Write the expressions that describe the length of each side of the pen.
  2. Build the equation that describes the area of the pen.
  3. To find the maximum area, use the vertex.
  4. Finally, use the -value from the vertex to find the lengths of each side of the pen.
This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit for more information.