Question

In an equilateral ∆ABC, D is the midpoint of AB and E is the midpoint of AC. Then, ar(∆ABC): ar(∆ADE) = ?

Options

• 2 : 1

• 4 : 1

• 1 : 2

• 1 : 4

Answer 1

4 : 1

Explanation:

Clearly, `(AD)/(AB) = (AE)/(AC) = 1/2` and ∠A = ∠A (common).

∴ ∆ABC ∼ ∆ADE   ...[By SAS-similarity].

∴ `ar(∆ABC) : ar(∆ADE) = ((AB)/(AD))^2`

= `(2/1)^2`

= `4/1`

= 4 : 1