1. **Problem 1:** Given two triangles ABC and CDE with ACE and BCD straight lines, AB parallel to DE, AC = 8 cm, CD = 15 cm, and DE = 20 cm, find the unknown side length $y = CB$. 2. Since AB is parallel to DE and triangles ABC and CDE share angle C, triangles ABC and CDE are similar by AA similarity. 3. The ratio of corresponding sides is $$\frac{AC}{CD} = \frac{8}{15}$$. 4. Using similarity, the ratio of sides CB to DE is the same: $$\frac{CB}{DE} = \frac{8}{15}$$. 5. Substitute DE = 20 cm: $$\frac{y}{20} = \frac{8}{15} \implies y = \frac{8}{15} \times 20 = \frac{160}{15} = 10.67 \text{ cm}$$. --- 6. **Problem 2:** Two similar triangles A and B have sides 7 m and 8 m in A, and 28 m and 32 m in B. The perimeter of triangle A is 22.5 m. Find the perimeter of triangle B. 7. Find the scale factor from triangle A to B using corresponding sides: $$\text{scale factor} = \frac{28}{7} = 4$$ (also check $$\frac{32}{8} = 4$$). 8. Since the triangles are similar, the perimeter scales by the same factor. 9. Calculate perimeter of B: $$\text{Perimeter}_B = 4 \times 22.5 = 90 \text{ m}$$. **Final answers:** - Unknown side $y = 10.67$ cm - Perimeter of triangle B = 90 m