Question : $\triangle ABC \sim \triangle DEF$ such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of $\triangle DEF = 25$ cm, then the perimeter of $\triangle ABC$ is:
Option 1: 40 cm
Option 2: 30 cm
Option 3: 35 cm
Option 4: 45 cm
Correct Answer: 35 cm
Solution :
Given, $\triangle ABC \sim \triangle DEF$
⇒ $\frac{\small\text{Perimeter of } \triangle ABC}{\small\text{Perimeter of }\triangle DEF}=\frac{AB}{DE}$
⇒ $\frac{\small\text{Perimeter of } \triangle ABC}{25}=\frac{9.1}{6.5}$
⇒ $\small\text{Perimeter of } \triangle ABC = \frac{9.1}{6.5}\times 25$
$\therefore \small\text{Perimeter of }\triangle ABC = 35$
Hence, the correct answer is 35 cm.
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