The perimeter of a square is half the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two- thirds of its length, then what is the area (in $m^2$) of the rectangle?

384

The perimeter of the square = 40 m

The perimeter of a square = half the perimeter of a rectangle.

The perimeter of the rectangle = 2 × 40 = 80 m

Let, the length of the rectangle be l

The breadth of the rectangle = \(\frac{2l}{3}\) 

Accordingly,

2 × ( x + \(\frac{2l}{3}\) ) = 80

= \(\frac{5l}{3}\) = 40

= l = 24

Length = \(\frac{2}{3}\) × 24 = 16 m

Area of the rectangle = (24 × 16) = 384 m²