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In triangle ABC, points D and E lie on sides AB and AC respectively with DE parallel to BC. Given AD = 4x - 3, AE = 8x - 7, BD = 3x - 1, and CE = 5x - 3, find x.

1. x = 1
2. x = 2
3. x = 3
4. x = 4

Correct answer: x = 1

Solution

Since DE is parallel to BC, the Basic Proportionality Theorem gives AD/DB = AE/EC. Cross-multiplying and simplifying produces a quadratic; the valid value (giving positive lengths) is x = 1.

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