The area of a square field is 5184 m². Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field and whose length is twice of its breadth.

Given, the area of a square field as 5184m²

We need to find out the area of a rectangular field.

We know that perimeter of a rectangular field = perimeter of the square field and length = twice breadth.

Now, Area of a square field = 5184m²

Area of a square = s × s, where s is side

⇒ = 72

Perimeter of a square field = 4 × s

= 4 × 72 = 288m

Perimeter of a square field = 288m = perimeter of a rectangular field.

Let breadth (b) = x and length (l) = 2x

We know that perimeter = 2 × (l + b)

= 2 × (2x + x)

= 2 × (3x)

= 6x

Here, 6x = 288m

⇒ 6x = 288

⇒ x =

⇒ x = 48m

Hence, breadth is 48m and length is 2 × 48 = 96m