1. **Problem Statement:** (i) Find the length of Site A along the lake shore. (ii) Find the length of Site C along the roadway. 2. **Given Data:** - Site A length along roadway: 9 m - Site B length along roadway: 7.2 m - Site C length along roadway: 8 m - Site A length along lake shore: unknown - Site C length along lake shore: 6.4 m 3. **Understanding the problem:** The sites form trapezoids or triangles between the roadway and lake shore. The lengths along the roadway and lake shore correspond to parallel sides. 4. **Step (i): Length of Site A along lake shore** - Site A along roadway = 9 m - Site B along roadway = 7.2 m - Site C along roadway = 8 m - Site C along lake shore = 6.4 m Assuming the lake shore and roadway are parallel, the ratio of lengths along the lake shore to roadway is constant for each site. Calculate the ratio for Site C: $$\text{Ratio} = \frac{\text{Lake shore length}}{\text{Roadway length}} = \frac{6.4}{8} = 0.8$$ Assuming the same ratio applies to Site A: $$\text{Site A lake shore length} = 9 \times 0.8 = 7.2\text{ m}$$ 5. **Step (ii): Length of Site C along roadway** Given directly as 8 m. --- 6. **Problem 10:** Given: $$|AB| = 5x, \quad |BC| = 3x, \quad |AD| = 4x - 3, \quad |DE| = 3x - 6$$ Since points A, B, C are collinear and D, E lie between them, the sum of segments must satisfy: $$|AB| + |BC| = |AD| + |DE| + |EC|$$ But since EC is not given, we use the fact that AD + DE = AB + BC (assuming D and E lie on the same line segment from A to C). Calculate: $$5x + 3x = (4x - 3) + (3x - 6)$$ $$8x = 7x - 9$$ $$8x - 7x = -9$$ $$x = -9$$ Since $x \in \mathbb{N}$, no negative solution. Check if problem expects positive $x$. 7. **Problem 11:** Given: $$|AD| = x, \quad |DB| = 10, \quad |BE| = x + 7, \quad |EC| = 6$$ Since points A, B, C are collinear and D, E lie on segments AB and BC respectively: $$|AB| = |AD| + |DB| = x + 10$$ $$|BC| = |BE| + |EC| = (x + 7) + 6 = x + 13$$ If AB and BC are equal (assuming triangle or trapezoid properties), then: $$x + 10 = x + 13$$ No solution. If not equal, no further info to solve for $x$. --- **Final answers:** (i) Length of Site A along lake shore = **7.2 m** (ii) Length of Site C along roadway = **8 m**