**Question:**

The area of a square field is 5184 cm2. A rectangular field, whose length is twice its breadth has its perimeter equal to the perimeter of the square field. Find the area of the rectangular field.

**Solution:**

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

The area of the square is* **r*2, 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