Q1. [1] § 6.1 Introduction § 6.4 Criteria for Similarity of Triangles § 6.5 Summary
In the given figure, $DE \parallel BC$. If $\dfrac{AD}{DB} = \dfrac{1}{3}$ and $AC = 6$ cm, then length $AE$ is
- A $1.5$ cm
- B $1$ cm
- C $2$ cm
- D $3$ cm
Previously asked in CBSE board exam
2026 30/4/1 Q6
Generated by claude-sonnet-4-6 · 2026-06-15 10:21 · grounding rag
Model Answer
By Basic Proportionality Theorem (DE ∥ BC), $\dfrac{AD}{DB} = \dfrac{AE}{EC} = \dfrac{1}{3}$.
So $AE = \dfrac{1}{4} \times AC = \dfrac{1}{4} \times 6 = \mathbf{1.5 \text{ cm}}$. → Option A
Explanation
Since AD/DB = 1/3, we get AD/AB = 1/4. By BPT, AE/AC = AD/AB = 1/4, giving AE = 1.5 cm. A common error is using AE/EC = 1/3 directly and stopping there — remember to find AE from AC, not EC.
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