If triangles ABC and PQR are similar and PQ = 2 cm, AB = 6 cm, BC = 9 cm, CA = 12 cm, then the perimeter of triangle PQR is:

As we know, two triangles are similar if

1. their corresponding angles are equal and
2. their corresponding sides are in the same ratio.

$\because △\mathrm{ABC}~△\mathrm{PQR}$   [Given]

$\therefore \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}=\frac{\mathrm{AC}}{\mathrm{PR}}$

$\Rightarrow \frac{6}{2}=\frac{9}{\mathrm{QR}}=\frac{12}{\mathrm{PR}}$

So, $\mathrm{QR}=\frac{2\times 9}{6}=3 \mathrm{cm}$

$\mathrm{PR}=\frac{2\times 12}{6}=4 \mathrm{cm}$

Therefore, the perimeter of the triangle PQR = PQ + QR + RP

= 2 + 3 + 4

= 9 cm