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D and E are points on the sides AB and AC respectively of ∆ABC such that DE is parallel to BC and AD : DB = 4 : 5, CD and BE intersect each other at F. Then find the ratio of the areas of ∆DEF and ∆CBF.
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- 16 : 25
- 16 : 81
- 81 : 16
- 4 : 9
- 16 : 25
Correct Option: B
DE || BC
∠ADE = ∠ABC
∠AED = ∠ACB
By AA–similarity. ∆ABC ~ ∆ADE
| ∴ | = | ||
| AB | BC |
| ∴ | = | ||
| AB | 5 |
| ⇒ | = | ||
| AD | 4 |
| ⇒ | = | ||
| AD | 4 |
| ⇒ | = | = | |||
| AD | 4 | DE |
∆DEF ~ ∆CBF
| ∴ | = | ||
| Area of ∆CBF | BC² |
| = | = 16 : 81 | |
| 81 |
