In, ΔABC, D and E are the mid-points of AB and AC respectively.

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In, ΔABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.

1. 1
  2
2. 1
  4
3. 3
  4
4. 1
  8
5. None of these

Correct Option: B

Clearly DE || BC (by converse of BPT) ∴ ΔADE ∼ ABC (∠A = ∠A and ∠ADE = ∠B)

∴	area (∆ADE)	=	AD²	(Area Theorem)
	area (∆ABC)		AB²

=	AD²	=	1	(∴AB = 2AD)
	(2AD)²		4