Question : If $\triangle ABC$~$\triangle PQR$, the ratio of perimeter of $\triangle ABC$ to perimeter of $\triangle PQR$ is 36 : 23 and QR = 3.8 cm, then the length of BC is:
Option 1: $4 \frac{103}{121} cm$
Option 2: $3 \frac{109}{121} cm$
Option 3: $5 \frac{109}{115} cm$
Option 4: $3 \frac{107}{115} cm$
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Correct Answer: $5 \frac{109}{115} cm$
Solution :
$\triangle ABC$~$\triangle PQR$
$\frac{BC}{QR}$ = $\frac{Perimeter(\triangle ABC)}{Perimeter(\triangle PQR)}$
$\frac{BC}{3.8}$ = $\frac{36}{23}$
BC = $\frac{36×38}{230}$
= $ \frac{684}{115}$
= $5 \frac{109}{115}$ cm
Hence, the correct answer is $5 \frac{109}{115}$ cm.
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