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In ∆ ABC, AB = 6 cms, BC = 10 cms, AC = 8cm and AD ⊥ BC. Find the value of the ratio of BD : DC.
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- 3 : 4
- 9 : 16
- 4 : 5
- 16 : 25
- 3 : 4
Correct Option: B
As per the given question , we draw a figure of right angled triangle CAB
Here , AB = 6 cms, BC = 10 cms, AC = 8cm and AD ⊥ BC
6² + 8² = 10²
∴ ∆ ABC is a right angled triangle.
| ∆ ABC = | × Base × Height | |
| 2 |
| ∴ | × AB × BC = | × BC × AD | ||
| 2 | 2 |
⇒ 6 × 8 = 10 × AD
| ⇒ AD = | cm. | |
| 5 |
Let BD = y cm.
From ∆ ABD,
| BD = √6² - |  |  | ² | |
| 5 |
| BD = √36 - | = √ | ||
| 25 | 25 |
| BD = √ | = | cm. | ||
| 25 | 5 |
| ∴ CD = 10 - | = | cm. | ||
| 5 | 5 |
| ∴ BD : CD = | : | = 9 : 16 | ||
| 5 | 5 |
