If the areas of two similar triangles are in the ratio $196 : 625$, what is the ratio of their corresponding sides?

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**Solution:**

1. According to the theorem, the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Let the areas be $A_1$ and $A_2$, and the corresponding sides be $s_1$ and $s_2$.

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

2. Given the ratio of areas:

$$\frac{A_1}{A_2} = \frac{196}{625}$$

3. To find the ratio of the sides, take the square root of both sides:

$$\frac{s_1}{s_2} = \sqrt{\frac{196}{625}} = \frac{\sqrt{196}}{\sqrt{625}} = \frac{14}{25}$$

**Answer:** The ratio of the corresponding sides is $14 : 25$.

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