I see the worksheet from Chapter 4 on problem-solving connections, focusing on proportions and scale models. Let me extract and analyze the relevant details to provide a solution.

Analysis:

1. Key Question 1A:

   • Write a proportion to find the width of the lake ($x$).
   • Using the figure, the proportion appears to relate smaller dimensions (scale) to actual dimensions. This could involve: $\frac{300}{15} = \frac{x}{9}$
   • This proportion compares the length and width in the model to those in the real lake.

2. Solving for $x$: Multiply both sides by 9 to solve for the unknown width $x$: $\frac{300}{15} = 20, \quad 20 \times 9 = 180 \quad \text{(width of the lake in feet)}.$

3. Key Question 1B:

   • Ratio of the length to width in the scale model. From the diagram, this would be: $\text{Length} : \text{Width} = 15 : 9 \quad \text{(Simplify to } 5 : 3\text{)}.$

4. Key Question 1C:

   • Length of the lake using proportions. The proportion relates the length and scale factor: $\frac{\text{Real Length}}{\text{Model Length}} = \frac{\text{Real Width}}{\text{Model Width}}$ This leads to similar calculations as in part (A).

Would you like a detailed explanation of each step, including further breakdowns of proportions and ratios?

Follow-Up Questions:

1. How are proportions used to solve real-world problems like this one?
2. What does the simplified ratio $5 : 3$ imply about the model dimensions?
3. How would this change if the model's scale were different (e.g., $20:1$)?
4. Could you reverse-engineer the dimensions of the lake using just the given model?
5. How do ratios simplify complex comparisons?

Tip:

When solving proportions, always cross-multiply carefully to avoid arithmetic errors.