Final answer:
The area of the rectangular field is calculated using the perimeter of a square field given its area. By finding the side length of the square and equating its perimeter to that of the rectangular field, we deduce the dimensions and area of the rectangular field. However, the calculated area does not match the provided options.
Step-by-step explanation:
To find the area of the rectangular field, we must first determine the side length of the square field whose area is 5184 m². The side of the square (s) can be found using the formula for the area of a square (A = s²), thus s = √5184 m = 72 m. The perimeter of the square is 4s, which equals 4 × 72 m = 288 m.
For the rectangular field, let the breadth be b and the length be 2b (since the length is twice the breadth). The perimeter of the rectangle is 2(b + 2b) = 6b. Since the perimeter of the rectangle equals that of the square, 6b = 288 m, so b = 48 m. The length is thus 2b = 96 m.
The area of the rectangular field (A_rect) is length × breadth, which gives A_rect = 96 m × 48 m = 4608 m².
This answer does not match any of the options provided, suggesting there may be an error in the question or answer choices. However, to resolve the issue, we should cross-check by calculating the perimeter of a rectangle with the given area options (assuming a 2:1 ratio of length to breadth) and comparing it to the perimeter of the square field to see if any match.