# The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively.

Question:

The perimeters of two similar triangles ABC and PQR are 32 cm and 24 cm respectively. If PQ = 12 cm. find AB.

Solution:

It is given that triangles ABC and PQR are similar.
Therefore,

$\frac{\text { Perimeter }(\triangle A B C)}{\text { Perimeter }(\triangle P Q R)}=\frac{A B}{P Q}$

$\Rightarrow \frac{32}{24}=\frac{A B}{12}$

$\Rightarrow A B=\frac{32 \times 12}{24}=16 \mathrm{~cm}$