**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 8**

**8.** 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**

**Given:** ABC and BDE are two equilateral triangles and D is the mid-point of BC.

Any two equilateral triangles are similar because each angle is equal to 60 degrees.

Therefore, ~

** (1)**

**{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}**

But, we have BC = 2BD because D is the mid-point of BC. ** (2)**

Putting **(2) in (1)**, we get

Therefore, answer is **(C)**