In the given figure, $\triangle AHK \sim \triangle ABC$. If $AK = 8$ cm, $BC = 3.2$ cm and $HK = 6.4$ cm, then find the length of $AC$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
Given: △AHK ~ △ABC, AK = 8 cm, BC = 3.2 cm, HK = 6.4 cm.
Since △AHK ~ △ABC, their corresponding sides are in the same ratio:
$$\frac{AK}{AC} = \frac{HK}{BC}$$
$$\frac{8}{AC} = \frac{6.4}{3.2}$$
$$\frac{8}{AC} = 2$$
$$AC = \frac{8}{2} = 4 \text{ cm}$$
Therefore, AC = 4 cm.
Source: Chapter 6, Section 6.3 – Similarity of Triangles
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Explanation
- In similar triangles, corresponding sides are proportional. Match vertices carefully: A↔A, H↔B, K↔C, so AK corresponds to AC, and HK corresponds to BC.
- Set up the ratio using the two known sides (HK and BC) to find the scale factor, then apply it to find AC.
- Examiners award 1 mark for the correct proportion and 1 mark for the correct answer.