Question

In a rectangle and square, the area of the rectangle is thrice that of the square. The length of the rectangle is 9 cm and the breadth is 16 times the length of a side of the square. Find the length of the side of the square in cm.

1. 48 cm
2. 50 cm
3. 45 cm
4. 25 cm

Answer 1

Correct Answer - Option 1 : 48 cm

Given:

The area of a rectangle is thrice the area of a square.

Length of the rectangle = 9 cm.

The breadth of the rectangle is 16 times the length of a side of the square.

Formula:

1) Let “a” and “b” be the length and the breadth of a rectangle,

   then  Area of rectangle = a × b

2) Area of a square = side²

Calculation:

Let “a” be the side of a square.

According to the question,

The area of the rectangle is thrice the area of the square.

9 × 16a = 3a²

⇒ 9 × 16 × a = 3 × a × a

⇒ a = 48

∴ The length of the side of the square is 48 cm.