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ABC is a triangle in which DE || BC and AD : DB = 5 : 4. Then DE : BC is
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- 4 : 5
- 4 : 9
- 9 : 5
- 5 : 9
- 4 : 5
Correct Option: D
On the basis of question we draw a figure of triangle ABC in which DE || BC ,
Given that , AD : DB = 5 : 4.
DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
By AA – similarly,
∆ ADE ~ ∆ ABC
| ∴ | = | ||
| AD | DE |
| ∴ | = | ||
| AD | 5 |
| ⇒ | + 1 = | + 1 | ||
| AD | 5 |
| ⇒ | = | ||
| AD | 5 |
| ⇒ | = | = | |||
| AD | 5 | DE |
| ∴ | = | = 5 : 9 | ||
| BC | 9 |
