Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.
Option 1: 18 cm
Option 2: 16 cm
Option 3: 20 cm
Option 4: 22 cm
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Correct Answer: 18 cm
Solution : $\triangle ABC \sim \triangle PQR$, $\therefore$ $\frac{AB}{BC} = \frac{PQ}{QR}$ And $\frac{AB}{AC} = \frac{PQ}{PR}$ $AB=4$ cm, $PQ=6$ cm, $QR=9$ cm, and $RP=12$ cm ⇒ $\frac{4}{BC} = \frac{6}{9}$ ⇒ $BC = 6$ cm ⇒ $\frac{4}{AC} = \frac{6}{12}$ ⇒ $AC = 8$ cm To find the perimeter of $\triangle \mathrm{ABC}$ $\therefore$ Perimeter = AB + BC + CA = 4 + 6 + 8 = 18 cm Hence, the correct answer is 18 cm.
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