Mathematics — Standard (041) — CBSE Class 10 board question

(B) $\dfrac{6}{7}$

Since △ABC ~ △PQR, the ratio of corresponding sides equals the ratio of their perimeters.

$$\frac{PQ}{AB} = \frac{\text{Perimeter of } \triangle PQR}{\text{Perimeter of } \triangle ABC} = \frac{48}{56} = \frac{6}{7}$$

For similar triangles, the ratio of any pair of corresponding sides equals the ratio of their perimeters. Here PQ corresponds to AB, so $\frac{PQ}{AB} = \frac{48}{56} = \frac{6}{7}$. A common mistake is inverting the ratio — always match numerator triangle to numerator perimeter.