In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
Since △ABC ~ △XYZ, corresponding sides are proportional:
$$\frac{AB}{XY} = \frac{BC}{YZ} = \frac{AC}{XZ}$$
$$\frac{4}{x} = \frac{6}{7.2} = \frac{y}{6}$$
From $\dfrac{6}{7.2}$:
$$\frac{4}{x} = \frac{6}{7.2} \Rightarrow x = \frac{4 \times 7.2}{6} = \frac{28.8}{6} = \mathbf{4.8 \text{ cm}}$$
$$\frac{y}{6} = \frac{6}{7.2} \Rightarrow y = \frac{6 \times 6}{7.2} = \frac{36}{7.2} = \mathbf{5 \text{ cm}}$$
Source: Chapter 6, Section 6.3 & 6.4
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Explanation
- In similar triangles, corresponding sides are in the same ratio — identify the correspondence carefully from the similarity statement (A↔X, B↔Y, C↔Z).
- Set up the proportion using all three pairs and solve cross-multiply for each unknown.
- Examiners expect the ratio setup written clearly before solving — don't just state the answer.