In $\triangle DEF$, AB $\parallel$ EF. The value of x is :
Generated by claude-sonnet-4-6 · 2026-06-15 10:25 · grounding rag
Model Answer
By Basic Proportionality Theorem (AB ∥ EF):
$$\frac{DA}{AE} = \frac{DB}{BF}$$
$$\frac{2x}{3x+1} = \frac{x}{2x - \frac{1}{2}}$$
Cross-multiplying:
$$2x\left(2x - \frac{1}{2}\right) = x(3x+1)$$
$$4x^2 - x = 3x^2 + x$$
$$x^2 - 2x = 0$$
$$x(x-2) = 0$$
So $x = 0$ or $x = 2$.
Since $x = 0$ gives zero length, x = 2.
Answer: (B) 2 only
Source: Triangles, Theorem 6.1 (Basic Proportionality Theorem), Chapter 6
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Explanation
- Apply BPT directly: since AB ∥ EF, the two sides DE and DF are divided in the same ratio.
- After solving the quadratic, both $x = 0$ and $x = 2$ satisfy the equation algebraically, but $x = 0$ makes segment DA = 0 (degenerate), so it is rejected.
- Examiners expect you to reject $x = 0$ with a reason — this is why the answer is "2 only," not "0, 2."