1. **State the problem:** We have two right triangles, one is a scaled copy of the other. The legs of the smaller triangle are both 15 units. The legs of the larger triangle are both $\frac{45}{2}$ units. We need to find the scale factor from the smaller triangle to the larger triangle and express it as a percent. 2. **Formula and rules:** The scale factor $k$ between two similar figures is the ratio of corresponding sides: $$k = \frac{\text{side length of larger triangle}}{\text{side length of smaller triangle}}$$ To express $k$ as a percent, multiply by 100. 3. **Calculate the scale factor:** $$k = \frac{\frac{45}{2}}{15}$$ 4. **Simplify the fraction:** $$k = \frac{45}{2} \times \frac{1}{15} = \frac{45}{2 \times 15} = \frac{45}{30}$$ 5. **Cancel common factors:** $$k = \frac{\cancel{15} \times 3}{\cancel{15} \times 2} = \frac{3}{2} = 1.5$$ 6. **Convert to percent:** $$1.5 \times 100 = 150\%$$ **Final answer:** The scale factor is 150%.