**Problem Analysis**

Let's assume the side length of the square field is 'x' meters. The area of a square is given by the formula A = x^2, where A is the area and x is the side length.

We are given that the area of the square field is 5184 m^2. Therefore, we can write the equation as:

x^2 = 5184

To find the side length 'x', we can take the square root of both sides of the equation. However, since we are looking for a positive value for the side length, we can ignore the negative square root. So,

x = √5184

Simplifying further, we get:

x = 72 meters

Now we need to find the dimensions of the rectangular field.

Let's assume the breadth of the rectangular field is 'b' meters. According to the problem, the length of the rectangular field is twice its breadth. Therefore, we can write the equation as:

Length = 2 * breadth

We know that the perimeter of a rectangle is given by the formula:

Perimeter = 2 * (Length + Breadth)

Since the perimeter of the rectangular field is equal to the perimeter of the square field, we can write the equation as:

2 * (2b + b) = 4 * 72

Simplifying further, we get:

6b = 288

Dividing both sides by 6, we get:

b = 48 meters

Therefore, the length of the rectangular field is:

Length = 2 * breadth = 2 * 48 = 96 meters

**Finding the Area of the Rectangular Field**

The area of a rectangle is given by the formula A = length * breadth. Therefore, we can calculate the area of the rectangular field as:

A = 96 * 48 = 4608 m^2

Therefore, the area of the rectangular field is 4608 m^2.