If △ABC ~ △PQR, area of △ABC = 81 cm², area of △PQR = 144 cm² and QR = 6 cm, then length of BC is

1. 4 cm

2. 4.5 cm

3. 9 cm

4. 12 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.

$\therefore \dfrac{\text{Area of △ABC}}{\text{Area of △PQR}} = \dfrac{BC^2}{QR^2} \\[1em] \Rightarrow \dfrac{BC^2}{6^2} = \dfrac{81}{144} \\[1em] \Rightarrow BC^2 = \dfrac{81 \times 36}{144} \\[1em] \Rightarrow BC^2 = \dfrac{2916}{144} \\[1em] \Rightarrow BC^2 = 20.25 \\[1em] \Rightarrow BC = \sqrt{20.25} \\[1em] \Rightarrow BC = 4.5$

∴ BC = 4.5 cm.

Hence, Option 2 is the correct option.