- A9 m
- B15 m
- C4 m
- D3.6 m
Step-by-Step Solution
m. By BPT, , so and m. 3.6 m comes from writing — BPT applied to the wrong pair of segments; 4 m comes from inverting the left ratio to ; 15 m is , which answers the wrong question.
Answer: A) 9 m
A triangular plot ABC is being developed. A straight drain DE is dug parallel to BC, with D on AB and E on AC. The measurements are AD = 12 m, AB = 20 m and EC = 6 m. Find AE.
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Basic Proportionality Theorem (BPT / Thales)
**Theorem**: If a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, then it divides them in the same ratio.
**Setup**: ΔABC. Line DE ∥ BC, with D on AB and E on AC.
**Conclusion**: AD/DB = AE/EC.
**Quick proof sketch**:
Draw DE ∥ BC. Triangles ADE and ABC have ∠A common and ∠ADE = ∠ABC (corresponding angles, DE ∥ BC). So ΔADE ~ ΔABC by AA.
Thus AD/AB = AE/AC.
From AD/AB = AE/AC, you can derive AD/DB = AE/EC by simple algebra.
**Converse**: if AD/DB = AE/EC, then DE ∥ BC.
Useful for proving lines parallel and finding lengths in triangles split by parallels.
**Setup**: ΔABC. Line DE ∥ BC, with D on AB and E on AC.
**Conclusion**: AD/DB = AE/EC.
**Quick proof sketch**:
Draw DE ∥ BC. Triangles ADE and ABC have ∠A common and ∠ADE = ∠ABC (corresponding angles, DE ∥ BC). So ΔADE ~ ΔABC by AA.
Thus AD/AB = AE/AC.
From AD/AB = AE/AC, you can derive AD/DB = AE/EC by simple algebra.
**Converse**: if AD/DB = AE/EC, then DE ∥ BC.
Useful for proving lines parallel and finding lengths in triangles split by parallels.
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