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ABCD is a trapezium in which AB||DC and AB = 2 CD. The diagonals AC and BD meet at O. The ratio of area of triangles AOB and COD is
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- 1 : 1
- 1 : √2
- 4 : 1
- 1 : 4
- 1 : 1
Correct Option: A
Let CD = x
⇒ AB = 2x. ∆ COD ~ ∆ AOB
because CD|| AB and take BD and AC as transversals.
| ∴ | = | = | = | ||||
| ar(AOB) | AB² | 4x² | 4 |
⇒ ∆ ABD – ∆ AOD
= ∆ ACB – ∆ BOC
⇒ ∆ AOB = ∆ AOB
| ⇒ | = | or 1 : 1 | ||
| ∆ COD | 1 |
