∆ABC ∼ ∆DEF and the perimeters of ∆ABC and ∆DEF are 30 cm and 18 cm respectively.
Question:

ABC ∼ ∆DEF and the perimeters of ∆ABC and ∆DEF are 30 cm and 18 cm respectively. If BC = 9 cm, then EF = ?
(a) 6.3 cm
(b) 5.4 cm
(c) 7.2 cm
(d) 4.5 cm

Solution:

(b) 5.4 cm

ABC ∼ ∆DEF

Therefore,

$\frac{\text { Perimeter }(\triangle A B C)}{\text { Perimeter }(\triangle D E F)}=\frac{B C}{E F}$

$\Rightarrow \frac{30}{18}=\frac{9}{E F}$.

$\Rightarrow E F=\frac{9 \times 18}{30}=5.4 \mathrm{~cm}$