If △ABC ~ △QRP, $\dfrac{\text{area of △ABC}}{\text{area of △PQR}} = \dfrac{9}{4}$, AB = 18 cm and BC = 15 cm, then the length of PR is equal to

1. 10 cm

2. 12 cm

3. $\dfrac{20}{3}$ cm

4. 8 cm

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.

$\therefore \dfrac{\text{Area of △ABC}}{\text{Area of △PQR}} = \dfrac{BC^2}{PR^2}$

Given, $\dfrac{\text{area of △ABC}}{\text{area of △PQR}} = \dfrac{9}{4}$.

So,

$\Rightarrow \dfrac{BC^2}{PR^2} = \dfrac{9}{4} \\[1em] \Rightarrow \dfrac{15^2}{PR^2} = \dfrac{9}{4} \\[1em] \Rightarrow PR^2 = \dfrac{225 \times 4}{9} \\[1em] \Rightarrow PR^2 = 100 \\[1em] \Rightarrow PR = \sqrt{100} \\[1em] \Rightarrow PR = 10.$

∴ PR = 10 cm.

Hence, Option 1 is the correct option.