Question : $\triangle ABC \sim \triangle DEF$ and the perimeters of $\triangle ABC$ and $\triangle DEF$ are 40 cm and 12 cm respectively. If DE = 6 cm then AB is:
Option 1: 12.6 cm
Option 2: 24 cm
Option 3: 20 cm
Option 4: 10 cm
Correct Answer: 20 cm
Solution :
Given: $\triangle ABC \sim \triangle DEF$
The perimeters of $\triangle A B C$ and $\triangle DEF$ are 40 cm and 12 cm
DE = 6 cm
If two triangles are similar, then the ratio of their corresponding sides is equal to the ratio of the corresponding perimeter.
$\frac{AB}{6}=\frac{40}{12}$
⇒ $AB=\frac{10}{3}×6$
⇒ AB = 20 cm
Hence, the correct answer is 20 cm.
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