1. **Problem 4:** Given two similar figures with corresponding side lengths, find the length $x$. 2. The figures are similar, so corresponding sides are proportional. The formula for similarity is: $$\frac{\text{side}_1}{\text{side}_2} = \frac{\text{corresponding side}_1}{\text{corresponding side}_2}$$ 3. Using the given lengths, set up the proportion for the lengths involving $x$: $$\frac{8}{10} = \frac{15}{x}$$ 4. Cross-multiply: $$8 \times x = 10 \times 15$$ $$8x = 150$$ 5. Divide both sides by 8 to solve for $x$: $$x = \frac{150}{8}$$ 6. Show cancellation: $$x = \frac{\cancel{150}}{\cancel{8}}$$ 7. Simplify the fraction: $$x = 18.75$$ --- 8. **Problem 6:** A scale model shows a 21-foot building as 3 inches tall. Find the model height for an 84-foot building. 9. Use the scale ratio: $$\frac{\text{model height}}{\text{actual height}} = \frac{3}{21}$$ 10. Let $h$ be the model height for the 84-foot building: $$\frac{h}{84} = \frac{3}{21}$$ 11. Cross-multiply: $$21h = 3 \times 84$$ $$21h = 252$$ 12. Divide both sides by 21: $$h = \frac{252}{21}$$ 13. Show cancellation: $$h = \frac{\cancel{252}}{\cancel{21}}$$ 14. Simplify: $$h = 12$$ **Final answers:** - Length $x = 18.75$ inches - Model height for 84-foot building = 12 inches