What dimensions will maximize the total area of the pen?

Question

A farmer builds a rectangular grid of pens with 1 row and 7 columns using 400 feet of fencing. What dimensions will maximize the total area of the pen?

 

The total width of each row of the pens should be?

the total height of column of pens should be?

which gives the maximum area of___ in square feet? 

Answer 1

With a given perimeter the rectangle with the greatest area is the square.

The farmer should make 7 square pens. The pens need 22 sides. Each side is 400/22 feet, or 200/11 feet.

The area of each pen is (200/11)² ft², or 1322.31 ft².

The area of all pens is 7(1322.31)ft², or 9256 ft².