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,
$\frac{\text { Perimeter }(\triangle A B C)}{\text { Perimeter }(\triangle D E F)}=\frac{B C}{E F}$
$\Rightarrow \frac{30}{18}=\frac{9}{E F}$.
$\Rightarrow E F=\frac{9 \times 18}{30}=5.4 \mathrm{~cm}$
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