The perimeter of a square is the same as the perimeter of a rectangle. The perimeter of the square is 40 m. If its breadth is two-thirds of its length, then the area (in m²) of the rectangle is:

96

We know that,

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth 

We have,

Perimeter of square = 40 m

Breadth of rectangle = Two-third of its length

The perimeter of square = Perimeter of rectangle

Let the length rectangle = 3a

Breadth = \(\frac{2}{3}\) × 3a = 2a

Perimeter = 2 × (Length + Breadth) = 40 = 2 × (3a + 2a)

= 20 = 5a

= a = 4

Length = 3a = 12 m

Breadth = 2a = 8 m

Area = Length × Breadth 

= Area = 12 × 8 = 96 m²