The sides of two similar triangles are in the ratio 3:7. The ratio of areas of these triangles will be :

Options

A. `1.5 : 3.5`
B. `9 : 49`
C. `6:14`
D. `49:4`

Answer

To find the ratio of the areas of two similar triangles when the ratio of their corresponding sides is given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ratio of the Sides**:
The sides of the two similar triangles are given in the ratio \(3:7\). This means:
\[ \text{Ratio of sides} = \frac{3}{7} \]

2. **Use the Property of Similar Triangles**:
For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Therefore, if the ratio of the sides is \( \frac{a}{b} \), then the ratio of the areas will be:
\[ \text{Ratio of areas} = \left(\frac{a}{b}\right)^2 \]

3. **Calculate the Ratio of Areas**:
Substitute the ratio of the sides into the formula:
\[ \text{Ratio of areas} = \left(\frac{3}{7}\right)^2 = \frac{3^2}{7^2} = \frac{9}{49} \]

4. **Final Result**:
Thus, the ratio of the areas of the two triangles is:
\[ \text{Ratio of areas} = \frac{9}{49} \]

### Conclusion:
The ratio of the areas of the two similar triangles is \(9:49\).

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