Question : $\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$ and the perimeters of these triangles are 32 cm and 12 cm, respectively. If $\mathrm{DE}=6 \mathrm{~cm}$, then what will be the length of AB?
Option 1: 16 cm
Option 2: 14 cm
Option 3: 12 cm
Option 4: 18 cm
Correct Answer: 16 cm
Solution :
If two triangles are similar, then their perimeters are directly proportional to the length of their corresponding sides.
So, $\frac{\text{Perimeter of $\triangle$ABC}}{\text{Perimeter of $\triangle$ABC}}= \frac{AB}{DE} = \frac{32}{12}$
⇒ $AB = \frac{32}{12}\times 6$
⇒ $AB = 16\ \mathrm{cm}$
Hence, the correct answer is 16 cm.
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