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# Tick the correct answer and justify :

Sides of two similar triangles are in the ratio 4: 9. Areas of these triangles are in the ratio.

(A) 2 : 3 (B) 4: 9 (C) 81: 16 (D) 16: 81

**Solution:**

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

Given that,

Sides of two similar triangles are in the ratio 4: 9.

We know that,

The ratio of the areas of two similar triangles = square of the ratio of their corresponding sides

= (4: 9)^{2}

= 16 : 81

Thus option (D) 16: 81 is the correct answer.

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

**Video Solution:**

## Sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio (A) 2 : 3 (B) 4: 9 (C) 81: 16 (D) 16: 81

NCERT Class 10 Maths Solutions Chapter 6 Exercise 6.4 Question 9

**Summary:**

The sides of two similar triangles are in the ratio 4:9. Areas of these triangles are in the ratio 16: 81.

**☛ 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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