1. **Problem Statement:** Find the scale factor of the sides for the similar triangles $\triangle KLI \sim \triangle TUV$. 2. **Understanding Similar Triangles:** When two triangles are similar, their corresponding sides are proportional. The scale factor $k$ is the ratio of any pair of corresponding sides. 3. **Identify Corresponding Sides:** From the notation $\triangle KLI \sim \triangle TUV$, the correspondence is: - $K \leftrightarrow T$ - $L \leftrightarrow U$ - $I \leftrightarrow V$ 4. **Use the Scale Factor Formula:** $$ k = \frac{\text{side in } \triangle TUV}{\text{corresponding side in } \triangle KLI} $$ 5. **Given Data:** Assuming the sides are labeled or given (not explicitly stated in the problem), let's say: - Side $KL$ corresponds to $TU$ - Side $LI$ corresponds to $UV$ - Side $KI$ corresponds to $TV$ 6. **Calculate the Scale Factor:** If the problem provides any side lengths, plug them in here. Since the problem does not provide explicit lengths, the scale factor is expressed as: $$ k = \frac{TU}{KL} = \frac{UV}{LI} = \frac{TV}{KI} $$ 7. **Conclusion:** The scale factor of the sides between $\triangle KLI$ and $\triangle TUV$ is the ratio of any pair of corresponding sides as shown above. If specific side lengths are provided, substitute them to find the numerical value of $k$.