Question : The perimeter of two similar triangles $\Delta \mathrm{ABC}$ and $\Delta\mathrm{ PQR}$ are $60\;\mathrm{cm}$ and $36\;\mathrm{cm}$ respectively. If $\mathrm{PQ} = 18\;\mathrm{ cm}$, then $\mathrm{AB}$ is:
Option 1: $20\;\mathrm{cm}$
Option 2: $24\;\mathrm{cm}$
Option 3: $36\;\mathrm{cm}$
Option 4: $30\;\mathrm{cm}$
Correct Answer: $30\;\mathrm{cm}$
Solution :
Given: The perimeter of two similar triangles $\Delta \mathrm{ABC}$ and $\Delta\mathrm{ PQR}$ are $60\;\mathrm{cm}$ and $36\;\mathrm{cm}$ respectively. The length of $\mathrm{PQ} = 18\;\mathrm{ cm}$.
Since the ratio of the corresponding sides of similar triangles is the same as the ratio of their perimeters.
$⇒\frac{\mathrm{AB}}{\mathrm{PQ}} = \frac{\text{Perimeter of $\Delta$ ABC}}{\text{Perimeter of $\Delta$ PQR}}$
$⇒\frac{\mathrm{AB}}{18\;\mathrm{ cm}} = \frac{60\;\mathrm{ cm}}{36\;\mathrm{ cm}}$
$⇒\mathrm{AB} = 30\;\mathrm{ cm}$
Hence, the correct answer is $30\;\mathrm{ cm}$.
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