Question

The Denver Aquarium is installing a new 1,600sf river otter exhibit and wants to minimize the number of materials used so that they can use the extra money on fun amenities for the otters. What is the minimum perimeter that can be used to achieve the 1,600sf area required for this exhibit? Describe the shape and explain your thinking.

Answer 1

The minimum perimeter for a 1,600-square-foot area is achieved with a square shape. The side length of the square is 40 feet, leading to a minimum perimeter of 160 feet. A square has the least perimeter for a given area due to the isoperimetric inequality.

Step-by-step explanation:

The minimum perimeter for a given area is achieved with a square shape. To find the perimeter of the square that would enclose a 1,600 square-foot area for the Denver Aquarium's river otter exhibit, we first calculate the side length of the square by taking the square root of the area. Since Area = side × side (or side2), we can find the side length of the square by computing the square root of 1,600 square feet, which is 40 feet. Therefore, the perimeter of the square would be 4 × side, which equals 4 × 40 feet or 160 feet.

By choosing a square shape, we minimize the perimeter for the 1,600 square foot area, which allows the Denver Aquarium to save on materials and spend more on amenities for the otters. This is because the square is the shape with the least perimeter for a given area, which is a consequence of the isoperimetric inequality.