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Mathematics — CBSE Class 10 board question

Q1. [1]
The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. $\frac{PQ}{AB}$ is equal to
  1. (A) $\frac{7}{8}$
  2. (B) $\frac{6}{7}$
  3. (C) $\frac{7}{6}$
  4. (D) $\frac{8}{7}$
Previously asked in CBSE board exam
2024 30/2/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer

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

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

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

Explanation

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.

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