Q1. [1] § 6.1 Introduction § 6.3 Similarity of Triangles § 6.5 Summary
In the given figure, $\triangle ABC \sim \triangle QPR$. If $AC = 6$ cm, $BC = 5$ cm, $QR = 3$ cm and $PR = x$; then the value of $x$ is :
- (a) $3.6$ cm
- (b) $2.5$ cm
- (c) $10$ cm
- (d) $3.2$ cm
Previously asked in CBSE board exam
2023 30/4/1 Q12
Generated by claude-sonnet-4-6 · 2026-06-15 10:24 · grounding rag
Model Answer
(b) 2.5 cm
Since △ABC ~ △QPR, corresponding sides are proportional:
$$\frac{BC}{PR} = \frac{AC}{QR}$$
$$\frac{5}{x} = \frac{6}{3}$$
$$x = \frac{5 \times 3}{6} = 2.5 \text{ cm}$$
Source: Chapter 6, Section 6.4 (Criteria for Similarity of Triangles)
Explanation
The key step is identifying correct corresponding sides from the similarity statement △ABC ~ △QPR: A↔Q, B↔P, C↔R. So AC corresponds to QR, and BC corresponds to PR. Examiners expect students to read the correspondence carefully from the order of vertices, not guess from the figure.
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