Question

$\left(△ABCand△BDE\right)$ are two equilateral traingles such that D is the midpoint of BC.Then,ar$\left(△BDE\right)$:ar$\left(△ABC\right)$=?

(a) 1:2

(b) 1:4

(c) $\sqrt{3}:2$

(d) 3:4

Answer 1

NSWER:
(b) 1:4
∆ ABC and ∆ BDE are two equilateral triangles​ and D is the midpoint of BC.
Let AB = BC = AC = a
Then BD = BE = ED = a/2
∴ ar(∆BDE)ar(∆ABC)= 14
So, required ratio = 1 : 4