Question

You have a 1200ft. roll of fencing. In a large field you want to make two paddocks by dividing a rectangle into two equal spaces. Find the dimensions of the largest such enclosure that you can make to maximize area.

Answer 1

To maximize the area of the enclosure, the dimensions of the largest rectangle should be 300 ft by 300 ft, resulting in an area of 90,000 square feet.

Step-by-step explanation:

To maximize the area of the enclosure, we need to find the dimensions of the largest rectangle that can be made using the 1200 ft. of fencing. Let's assume the length of one side of the rectangle is x ft. This means the length of the other side will also be x ft.

The perimeter of the rectangle is given by 2x + 2x = 4x. Since the total length of the fencing is 1200 ft, we have 4x = 1200 ft. Solving for x, we get x = 300 ft.

Therefore, the dimensions of the largest rectangle enclosure that can be made are 300 ft by 300 ft, resulting in an area of 300 ft x 300 ft = 90,000 square feet.