If the areas of two similar triangles are in the ratio $121 : 225$, what would be the ratio of the corresponding sides?

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**Solution:**

1. Given the ratio of areas of two similar triangles is $121 : 225$.

2. For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides:

$$\left( \frac{s_1}{s_2} \right)^2 = \frac{A_1}{A_2} = \frac{121}{225}$$

3. Taking the square root on both sides:

$$\frac{s_1}{s_2} = \sqrt{\frac{121}{225}} = \frac{11}{15}$$

4. Therefore, the ratio of the corresponding sides is $11 : 15$.

**Answer:** $11 : 15$

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