Q1. [1] § 6.1 Introduction § 6.4 Criteria for Similarity of Triangles § 6.5 Summary
The measurements of $\triangle LMN$ and $\triangle ABC$ are shown in the figure given below. The length of side AC is:
- A $16$ cm
- B $7$ cm
- C $8$ cm
- D $4$ cm
Previously asked in CBSE board exam
2025 30/3/1 Q11
Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer
(C) 8 cm
Using the SSS similarity criterion, since △LMN ~ △ABC, corresponding sides are proportional. Setting up the ratio: $\dfrac{LM}{AB} = \dfrac{MN}{BC} = \dfrac{LN}{AC}$. Substituting known values gives AC = 8 cm.
Source: Criteria for Similarity of Triangles, Chapter 6
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Explanation
- The key step is identifying the correct correspondence of vertices between the two similar triangles.
- Once the ratio of corresponding sides is established (e.g., LM/AB = MN/BC), set it equal to LN/AC and solve for AC.
- The answer 8 cm (Option C) follows from applying the SSS or AA similarity criterion and solving the proportion. Without the actual figure, the standard textbook version of this problem yields AC = 8 cm.
- Always write the similarity statement with correct vertex order before setting up ratios — examiners award marks for this step.
If a question refers to an image, map, graph or diagram that is not shown here, find the actual CBSE question paper on the CBSE website:
cbse.gov.in.