It is given that △ABC ~ △PQR with $\dfrac{BC}{QR} = \dfrac{1}{3}$, then $\dfrac{\text{area of △PQR}}{\text{area of △ABC}}$ is equal to

1. 9

2. 3

3. $\dfrac{1}{3}$

4. $\dfrac{1}{9}$

Given $\dfrac{BC}{QR} = \dfrac{1}{3}$

So, $\dfrac{QR}{BC} = \dfrac{3}{1}$.

Since triangles are similar. We know that, the ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

$\therefore \dfrac{\text{Area of △PQR}}{\text{Area of △ABC}} = \dfrac{QR^2}{BC^2} \\[1em] = \dfrac{3^2}{1^2} \\[1em] = \dfrac{9}{1} \\[1em] = 9.$

Hence, Option 1 is the correct option.