1. **State the problem:** We are given two similar kites with corresponding side lengths. We need to calculate the scale factor between the original kite and the transformed kite and then use it to find missing side lengths. 2. **Calculate the scale factor using sides DE and D'E':** Given side DE = 14 in and side D'E' = 5.6 in. The scale factor is the ratio of the transformed side length to the original side length: $$\text{scale factor} = \frac{\text{side D'E'}}{\text{side DE}} = \frac{5.6}{14} = \frac{2}{5}$$ Since the transformed kite is smaller, the scale factor is between 0 and 1, which fits the problem. 3. **Use the scale factor to find the transformed length of side CD:** Given side CD = 24 in. Calculate side C'D' as: $$\text{side C'D'} = \text{side CD} \times \text{scale factor} = 24 \times \frac{2}{5}$$ Show intermediate cancellation: $$24 \times \frac{2}{5} = \frac{\cancel{24} \times 2}{\cancel{5}} = \frac{24 \times 2}{5} = 9.6$$ So, side C'D' = 9.6 in. 4. **Check the result:** The calculated side C'D' = 9.6 in matches the given side length of the transformed kite, confirming the scale factor and calculations are correct. **Final answer:** The scale factor is $\frac{2}{5}$ and the transformed side length C'D' is 9.6 in.