Find the dimensions of a rectangular corral split into 2 pens of the same size producing the greatest possible
enclosed area given 300 feet of fencing.
Width help (numbers)
Length

Let’s set up a situation where the total fencing of 300 feet is used wisely! If you have a rectangular corral split into two equal pens, you’ll need to account for both the outer fencing and the interior divider.

Let’s denote the length of the rectangular corral as and the width as . The equation for the total perimeter, considering the divider, can be written as:

From this, we can solve for in terms of :

To maximize the enclosed area of the corral, we express it as:

This function can be optimized using calculus or by completing the square to find that maximizes area.

Once the optimal is determined, you can find the corresponding using the perimeter equation. The result will give you the perfect dimensions for your corral, ensuring that you get the most out of that 300-foot fencing! Happy pen building!