Question : $\Delta ABC$ and $\Delta DEF$ are similar. Also $\angle A=\angle D$ and $\angle B=\angle E$. If $4AB=DE$ and $BC=\operatorname{12 cm}$, then $EF$ is equal to:
Option 1: $\operatorname{3 cm}$
Option 2: $\operatorname{24 cm}$
Option 3: $\operatorname{16 cm}$
Option 4: $\operatorname{48 cm}$
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Correct Answer: $\operatorname{48 cm}$
Solution :
Given that $\Delta ABC\sim\Delta DEF$ and $4AB = DE$
Since the triangles are similar, the ratios of their corresponding sides are equal.
$\frac{BC}{EF} = \frac{AB}{DE}$
$⇒\frac{12}{EF} = \frac{AB}{4AB}=\frac{1}{4}$
$\therefore EF = 12×4 = \operatorname{48 cm}$
Hence, the correct answer is $\operatorname{48 cm}$.
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