The ratio of length and breadth of a rectangle is 3 : 2 respectively. The respective ratio of its perimeter and area is 5 : 9. What is the breadth of the rectangle in metres ?

Answer: Option A

Let the length and breadth of the rectangle be 3x and 2x respectively
Then,
Perimeter = 2 (3x + 2x) = 10x
And,
Area = (3x × 2x) = 6x²
$$\begin{array}{rl}& \therefore \frac{10x}{6x^2}=\frac{5}{9}\\ & \Rightarrow 30x=90\\ & \Rightarrow x=3\end{array}$$
So, breadth = (2 × 3) m = 6 m