The area of a square field is 5184 cm

Solution:

First, we have to find the perimeter of the square.

The area of the square is r2, where r is the side of the square.

Then, we have the equation as follows:

r2 = 5184 = (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x (3 x 3)

Taking the square root, we get r = 2 x 2 x 2 x 3 x 3 = 72

Hence the perimeter of the square is 4 x r = 288 m

Now let L be the length of the rectangular field.

Let W be the width of the rectangular field.

The perimeter is equal to the perimeter of square. 

Hence, we have:

2(L + W) = 288

Moreover, since the length is twice the width:

L = 2 x W.

Substituting this in the previous equation, we get:

2 x (2 x W + W) = 288

3 x W = 144

W = 48

To find L:

L = 2 x W = 2 x 48 = 96

∴ Area of the rectangular field = L x W = 96 x 48 = 4608 m2