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If $\triangle ABC \sim \triangle DEF$ and AB = $4$ cm, DE = $6$ cm, EF = $9$ cm and FD = $12$ cm, find the perimeter of $\triangle ABC$.
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Given, $$\begin{aligned}& \triangle ABC \sim \triangle DEF \\ & \therefore \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{DF} \\ & \Rightarrow \frac{4}{6} = \frac{BC}{9} = \frac{CA}{12} \\ & \therefore BC = 6\end{aligned}$$ cm and CA = $8$ cm
Perimeter of $\triangle ABC = 4+6+8=18$ cm
Perimeter of $\triangle ABC = 4+6+8=18$ cm