The length and the breadth of a rectangle are in the ratio 9 : 5. If its area is 180 m²; the length (longest side) of the rectangle is :

1. 36 m

2. 20 m

3. 10 m

4. 18 m

Given:

The length and the breadth of a rectangle are in the ratio 9 : 5.

The area of the rectangle is 180 m².

Let the length of the rectangle be 9a and the breadth of the rectangle be 5a.

As we know, the area of the rectangle = length x breadth

⇒ 180 m² = 9a x 5a

⇒ 180 m² = 45a²

⇒ a² = $\dfrac{180}{45}$ m²

⇒ a² = 4 m²

⇒ a = $\sqrt{4}$ m

⇒ a = 2 m

So, the length of the rectangle is 9a.

= 9 x 2 m

= 18 m

Hence, option 4 is the correct option.