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# 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} (Since D is the midpoint of BC)

= [(BC)^{2} × 4] / (BC)^{2}

= 4

Thus, Area ΔABC : Area ΔBDE = 4 : 1

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

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 6

**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

**Summary:**

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

**☛ Related Questions:**

- If the areas of two similar triangles are equal, prove that they are congruent.
- D, E and F are respectively the mid-points of sides AB, BC and CA of ∆ ABC. Find the ratio of the areas of ∆ DEF and ∆ ABC
- Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
- Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.

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