Final answer:
Jay can create a larger area by arranging 18 feet of fencing into a square, with each side measuring 4.5 feet. This results in a square with an area of 20.25 square feet, versus the rectangle's area of 20 square feet.
Step-by-step explanation:
To determine if Jay could make a larger area by arranging 18 feet of fencing into a square instead of a rectangle, we first need to calculate the areas of both shapes. Currently, Jay has a rectangle that is 5 feet long and 4 feet wide. The area of this rectangle is length × width, which equals 5 feet × 4 feet = 20 square feet.
Next, we'll find the dimensions of a square that could be made with the same amount of fencing. As fencing is the perimeter of the shape, and all four sides of a square are equal, we divide the total length of fencing by 4 to find the length of each side. This gives us 18 feet ÷ 4 = 4.5 feet per side for the square.
We then calculate the area of the square: side length squared, which is 4.5 feet × 4.5 feet = 20.25 square feet. Comparing the area of the square (20.25 square feet) with the area of the rectangle (20 square feet), we see that the square indeed provides a larger area with the same amount of fencing.