# 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:**

ΔABC is similar to ΔBDE (equilateral triangles are similar)

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

Area ΔABC / Area ΔBDE = (BC)^{2} / (BD)^{2}

= (BC)^{2} / (BC / 2)^{2} (D is the midpoint of BC)

= [(BC)^{2} × 4] / (BC)^{2}

= 4

Area ΔABC : Area ΔBDE = 4 : 1

Thus option (C) 4: 1 is the correct answer.

**Video Solution:**

## 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

### NCERT Class 10 Maths Solutions - Chapter 6 Exercise 6.4 Question 8:

Tick the correct answer and justify: ABC and BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangles ABC and BDE is (A) 2: 1 (B) 1: 2 (C) 4: 1 (D) 1: 4

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. The ratio of the areas of triangles ABC and BDE is 4:1