If $\triangle ABC \sim \triangle PQR$ in which $AB = 6$ cm, $BC = 4$ cm, $AC = 8$ cm and $PR = 6$ cm, then find the length of $(PQ + QR)$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:21 · grounding rag
Model Answer
Given: △ABC ~ △PQR, where AB = 6 cm, BC = 4 cm, AC = 8 cm, PR = 6 cm.
Since △ABC ~ △PQR, corresponding sides are in the same ratio:
$$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$$
$$\frac{6}{PQ} = \frac{4}{QR} = \frac{8}{6} = \frac{4}{3}$$
Finding PQ:
$$PQ = \frac{6 \times 3}{4} = \frac{18}{4} = 4.5 \text{ cm}$$
Finding QR:
$$QR = \frac{4 \times 3}{4} = 3 \text{ cm}$$
Therefore, $PQ + QR = 4.5 + 3 = \mathbf{7.5 \text{ cm}}$
Source: Chapter 6, Section 6.3 – Similarity of Triangles
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Explanation
- The key step is identifying correct correspondence: △ABC ~ △PQR means A↔P, B↔Q, C↔R, so AB/PQ = BC/QR = AC/PR.
- Use the known ratio AC/PR = 8/6 = 4/3 to find both PQ and QR.
- Examiners award 1 mark for setting up the correct ratio and 1 mark for the final answer. Don't mix up corresponding sides.