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In figure, DE || BC. If DE = 3 cm, BC = 6 cm and area of ∆ADE = 15 sq. cm, then the area of ∆ABC is
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- 75 sq. cm.
- 45 sq. cm.
- 30 sq. cm.
- 60 sq. cm.
- 75 sq. cm.
Correct Option: D
DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
By AA–similarity,
∆ADE ~ ∆ABC
| ∴ | = | ||
| Area of ∆ADE | DE² |
| ⇒ | = | ||
| 15 | 3² |
| = | = 4 | |
| 9 |
∴ Area of DABC = 4 × 15
= 60 sq. cm.
