How to Optimize the Area of a Rectangular Pig Pen
What is the problem related to a farmer and a rectangular pig pen?
A farmer has 120m of fencing to build a rectangular pig pen. The pen will have one internal fence dividing it into two equal sections. What are the dimensions that will produce the pen of maximum area?
Answer:
The dimensions that produce the pen of maximum area are 20 meters by 40 meters.
In order to find the dimensions that will result in the maximum area for the rectangular pig pen, we need to consider the given information. Let's denote the width of the pen as x meters. Since the pen is divided into two equal sections, the length will be 2x meters.
The perimeter of the pen is the sum of all the sides, which is given as 120 meters. Setting up the equation, we get:
2x + 2(2x) = 120
Solving the equation, we find that x = 20. Therefore, the width of the pen is 20 meters and the length is 40 meters.
Hence, the dimensions that will result in the maximum area for the rectangular pig pen are 20 meters by 40 meters.