Question

Many realworld problems involve the idea of optimization. In this activity, choose an animal that you need to make a rectangular fenced enclosure for. State what animal you chose and what the minimum required square footage (area) is for the fenced enclosure. Provide the width and length for 3 different possible configurations of your enclosure (different dimensions but the same square footage). Circle the configuration that requires the least amount of fencing to fence the perimeter of the enclosure. Based on your observations, determine if you can create another configuration that will be more optimal (use less fencing). If so, determine the dimensions that will use the least amount of fencing. Explain how you know that you have found the configuration that requires the least amount of fencing.

Answer 1

To determine the minimum required square footage of a rectangular fenced enclosure for an animal, consider the space required for the animal to move comfortably. Choose a configuration that requires the least amount of fencing by using a square shape with equal sides.

Step-by-step explanation:

To determine the minimum required square footage of a rectangular fenced enclosure for an animal, you need to consider the space required for the animal to move comfortably. Let's say we choose a dog as our animal. Dogs need space to run and play, so a minimum square footage of 100 square feet would be a good starting point.

Now, let's consider different configurations of the enclosure that have the same area of 100 square feet. One possible configuration could be a 10-foot by 10-foot square enclosure, which would require 40 feet of fencing. Another configuration could be a 5-foot by 20-foot rectangle, which would also require 40 feet of fencing. Finally, a 4-foot by 25-foot rectangle would have the same area and would require 58 feet of fencing.

Based on these configurations, we can see that the square enclosure with dimensions 10 feet by 10 feet requires the least amount of fencing. This is because all sides of the square enclosure are equal in length, so the perimeter is minimized.

It is not possible to find another configuration that uses less fencing than the square enclosure. This is because a square is always the most efficient shape in terms of perimeter for a given area. Any other shape with the same area will have a greater perimeter.