If $ riangle ABC$ and $ riangle DEF$ are similar such that $2AB =...

Question

If $	riangle ABC$ and $	riangle DEF$ are similar such that $2AB = DE$ and $BC = 8$ cm, then $EF$ is equal to:

Accepted Answer

Since $	riangle ABC \sim 	riangle DEF$, corresponding sides are proportional: $\frac{AB}{DE} = \frac{BC}{EF}$. Given $2AB = DE$, so $\frac{AB}{DE} = \frac{1}{2}$. Thus $\frac{BC}{EF} = \frac{1}{2} \Rightarrow EF = 2 	imes BC = 2 	imes 8 = 16$ cm.

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