[4 : 1] Tick the correct answer and justify :ABC and BDE are two equilateral triangles such that

For Competitive Exams

Tick the correct answer and justify :
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is

2 : 1

1 : 2

4 : 1

1 : 4

Explanation:

Given, ΔABC and ΔBDE are two equilateral triangle. D is the midpoint of BC.

∴ BD = DC = $\dfrac{1}{2BC}$

Let each side of triangle is 2a.

As, ΔABC ~ ΔBDE

$\dfrac{ Area(ΔABC)}{Area(ΔBDE)} = \dfrac{AB^2}{BD^2} = \dfrac{(2a)^2}{(a)^2} = \dfrac{4a^2}{a^2} = \dfrac{4}{1} = 4:1$

Hence, the correct answer is (C).

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