In the given figure, $\triangle AHK \sim \triangle ABC$. If AK = 10 cm, BC = 3·5 cm and HK = 7 cm, find the length of AC.
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
Given: △AHK ~ △ABC, AK = 10 cm, BC = 3.5 cm, HK = 7 cm.
Since △AHK ~ △ABC, corresponding sides are proportional:
$$\frac{AK}{AC} = \frac{HK}{BC}$$
$$\frac{10}{AC} = \frac{7}{3.5}$$
$$\frac{10}{AC} = 2$$
$$AC = \frac{10}{2} = 5 \text{ cm}$$
∴ AC = 5 cm
Source: Chapter 6, Section 6.3 – Similarity of Triangles
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Explanation
- Since △AHK ~ △ABC, the correspondence is A↔A, H↔B, K↔C. So the side AK (between A and K) corresponds to AC (between A and C), and HK corresponds to BC.
- Set up the ratio of corresponding sides and solve. The examiner expects you to clearly state which sides correspond and show the proportion step-by-step.