1. **State the problem:** We have two right triangles. The smaller triangle has legs 14 and 8 units. The larger triangle has legs 21 and 12 units, and a hypotenuse of 24 units. We need to find the scale factor from the smaller triangle to the larger triangle. 2. **Check if the triangles are similar:** For similarity, the ratios of corresponding sides must be equal. 3. **Calculate the ratio of the legs:** - Ratio of first legs: $\frac{21}{14} = 1.5$ - Ratio of second legs: $\frac{12}{8} = 1.5$ 4. **Check the hypotenuse of the smaller triangle:** Calculate the hypotenuse using Pythagoras theorem: $$\sqrt{14^2 + 8^2} = \sqrt{196 + 64} = \sqrt{260} \approx 16.12$$ 5. **Calculate the ratio of hypotenuses:** $$\frac{24}{16.12} \approx 1.49$$ 6. **Conclusion:** The ratios of corresponding sides are approximately equal (1.5), so the triangles are similar. 7. **Scale factor:** The scale factor from the smaller triangle to the larger triangle is approximately $1.5$. **Final answer:** The scale factor is $1.5$.