# 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 (a) 2 : 1 (b) 1 : 2 (c) 4 : 1 (d) 1 : 4

## Solution :

Since $$\triangle$$ ABC and BDE are equilateral triangles, they are equiangular and hence

$$\triangle$$ ABC ~ $$\triangle$$ BDE

So, $$area(\triangle ABC)\over area(\triangle BDE)$$ = $${BC}^2\over {BD}^2$$

or  $$area(\triangle ABC)\over area(\triangle BDE)$$ = $${2BD}^2\over {AC}^2$$

$$\implies$$  $$area(\triangle ABC)\over area(\triangle BDE)$$ = $$4\over 1$$

$$\therefore$$ (d) is the correct answer.