Geometry and TrigonometryVery hardSimilar triangles from a parallel segment
Geometry and Trigonometry practice question
In triangle ABC, point D lies on side AB and point E lies on side AC such that segment DE is parallel to side BC. If AD = 4, DB = 6 and DE = 6, what is the length of BC?
Answer: 15
Because DE ∥ BC, triangle ADE is similar to triangle ABC. The ratio of corresponding sides is AD/AB = 4/(4 + 6) = 4/10. So DE/BC = 4/10, giving BC = 6 × 10/4 = 15.
Common wrong answers
- If you answered 6
- 6 is DE itself. BC is the longer, corresponding side of the larger triangle.
- If you answered 9
- 9 uses DB/AD = 6/4 as the scale factor. The small triangle's side is AD = 4, and the whole side is AB = 4 + 6 = 10, so the scale factor is 10/4.
- If you answered 10
- 10 is the length of AB, not BC. BC corresponds to DE, scaled by 10/4.
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