Question

In a rectangle, the length is 20% more than the width and its perimeter is 220 cm. If the length of the rectangle is equal to the perimeter of the square, then find the area of the square.
1. 169 cm²
2. 196 cm2
3. 225 cm2
4. 100 cm2
5. 256 cm2

Answer 1

Correct Answer - Option 3 : 225 cm2

GIVEN :

The length of the rectangle is 20% more than the width of the rectangle.

Perimeter of the rectangle = 220 cm

Length of the rectangle = Perimeter of the square

 

FORMULA USED :

Perimeter of the rectangle = 2 × (length + width)

Perimeter of the square = 4 × (side)

Area of the square = (side)²

 

ASSUMPTION :

Let the length and the width of the rectangle be '6x' and '5x'.

 

CALCULATION :

Perimeter of the rectangle = 220 cm

⇒ 2 × (length + width) = 220

⇒ 2 × (6x + 5x) = 220

⇒ x = 10

Length of the rectangle = 6x

⇒ 60 cm

Length of the rectangle = Perimeter of the square

⇒ 60 = 4 × (side)

⇒ side = 15 cm

Area of the square = (side)²

⇒ (15)²

⇒ 225 cm²

∴ The area of the square is 225 cm².