A rectangular frame of length 12 m is formed with a 40 m long wire. The wire is re-bent to form a square. Which of the following alternatives represents the correct statement?

It is given that a rectangular frame of length 12 m is formed with a 40 m long wire.

∴ Perimeter of the rectangle = 40 m

⇒ 2 (Length + Breadth) = 40 m

⇒ 12 m + Breadth = 20 m

⇒ Breadth = 20 m − 12 m = 8 m

∴ Area of rectangle = Length × Breadth = 12 m × 8 m = 96 sq. m

The perimeter of a square is also 40 m.

∴ 4 × Side of square = 40 m

⇒ Side of square = $\frac{40}{4}$m = 10 m

∴ Area of square = Side × Side = 10 m × 10 m = 100 sq. m

Therefore, difference between the areas = (100 sq. m − 96 sq. m) = 4 sq. m

Thus, the area of the square is 4 sq. m more than that of a rectangle.