Question : The perimeter of two similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ = 10 cm. then the length of AB is:
Option 1: 18 cm
Option 2: 12 cm
Option 3: 15 cm
Option 4: 30 cm
Correct Answer: 15 cm
Solution :
Since the ratio of the corresponding sides of similar triangles is the same as the ratio of their perimeters.
$\triangle{ABC} \sim\triangle{PQR}$
$\Rightarrow \mathrm{\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} = \frac{36}{24}}\\$
$\Rightarrow\mathrm{\frac{AB}{PQ} = \frac{36\;\mathrm{cm}}{24\;\mathrm{cm}}}\\$
$\Rightarrow \mathrm{\frac{AB}{10\;\mathrm{cm}} = \frac{36\;\mathrm{cm}}{24\;\mathrm{cm}}}\\$
$\Rightarrow \mathrm{AB = \frac{36\;\mathrm{cm} \times 10\;\mathrm{cm}}{24\;\mathrm{cm}} = 15\;\mathrm{cm}}$
Hence, the correct answer is 15 cm.
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