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

Options

A. 2:3
B. 4:9
C. 18:16
D. 16: 81

Answer

To solve the problem, we need to find the ratio of the areas of two similar triangles given that their sides are in the ratio of 4:9.

### Step-by-step Solution:

1. **Understand the relationship between the sides and areas of similar triangles**:
- For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

2. **Identify the ratio of the sides**:
- The sides of the two triangles are given in the ratio 4:9.

3. **Set up the ratio of the areas**:
- Let the ratio of the sides be represented as:
\[ \text{Ratio of sides} = \frac{4}{9} \]
- According to the property mentioned, the ratio of the areas will be:
\[ \text{Ratio of areas} = \left(\frac{4}{9}\right)^2 \]

4. **Calculate the square of the ratio**:
- Now, calculate the square of the ratio:
\[ \left(\frac{4}{9}\right)^2 = \frac{4^2}{9^2} = \frac{16}{81} \]

5. **Conclusion**:
- Therefore, the ratio of the areas of the two triangles is:
\[ \frac{16}{81} \]

### Final Answer:
The areas of the triangles are in the ratio \( \frac{16}{81} \).

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