ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the area of triangles ABC and BDE is
(A) 2 : 1
(B) 1 : 2
(C) 4 : 1
(D) 1 : 4

Given, \(\triangle\) ABC and \(\triangle\) BDE are two equilateral triangle. D is the midpoint of BC.

BD = DC = 1/2BC
Let each side of triangle is 2a.
As, \(\triangle\) ABC ~ \(\triangle\) BDE
Area(\(\triangle\) ABC)/Area(\(\triangle\) BDE) = \(AB^/BD^2 = (2a)^2/(a)^2 \)b
\(= 4a^2/a^2 = 4/1 = 4:1\)
Hence, the correct answer is (C).