6. \( \triangle A B C \) has side lengths 42,21 , and 35 units. The shortest side of a triangle similar to \( \triangle A B C \) is 9 units long. Find the other lengths of the triangle.

To determine the lengths of the other sides in a triangle similar to \( \triangle ABC \), follow these steps: 1. **Identify the Scale Factor:** - The original triangle \( \triangle ABC \) has sides of lengths 42, 21, and 35 units. - The shortest side in \( \triangle ABC \) is 21 units. - In the similar triangle, the shortest side is given as 9 units. - **Scale Factor** \( k = \frac{9}{21} = \frac{3}{7} \). 2. **Apply the Scale Factor to the Other Sides:** - **Second Side:** \[ 35 \times \frac{3}{7} = 15 \text{ units} \] - **Third Side:** \[ 42 \times \frac{3}{7} = 18 \text{ units} \] 3. **Conclusion:** - The lengths of the other sides in the similar triangle are **15 units** and **18 units**. **Final Answer:** A similar triangle with shortest side 9 has the other sides equal to 15 and 18 units.