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# 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.
As, $$\triangle$$ ABC ~ $$\triangle$$ BDE
Area($$\triangle$$ ABC)/Area($$\triangle$$ BDE) = $$AB^/BD^2 = (2a)^2/(a)^2$$b
$$= 4a^2/a^2 = 4/1 = 4:1$$