Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length of the Panama Canal is 82 kilometers. What is the l... Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length of the Panama Canal is 82 kilometers. What is the length in centimeters of the Panama Canal on Ana's map?
Understand the Problem
The question is asking for the length of the Panama Canal on Ana's map based on the given scale, where 4 centimeters represents 20 kilometers. The actual length of the Panama Canal is 82 kilometers. We need to convert this to centimeters on the map using the scale provided.
Answer
The length of the Panama Canal on Ana's map is $16.4 \text{ cm}$.
Answer for screen readers
The length of the Panama Canal on Ana's map is $16.4 \text{ cm}$.
Steps to Solve
- Determine the scale ratio
The scale states that 4 centimeters on the map represents 20 kilometers in reality. We can find the ratio of centimeters to kilometers:
$$ \text{Ratio} = \frac{4 \text{ cm}}{20 \text{ km}} = \frac{1 \text{ cm}}{5 \text{ km}} $$
- Calculate the length in centimeters for 82 kilometers
To find the length of the Panama Canal on Ana's map (which is 82 km in reality), we use the ratio we found. We need to find how many centimeters represent 82 kilometers:
$$ \text{Length in cm} = 82 \text{ km} \times \frac{1 \text{ cm}}{5 \text{ km}} $$
Simplifying this gives:
$$ \text{Length in cm} = \frac{82}{5} \text{ cm} = 16.4 \text{ cm} $$
- Final result
The length of the Panama Canal on Ana's map is therefore:
$$ 16.4 \text{ cm} $$
The length of the Panama Canal on Ana's map is $16.4 \text{ cm}$.
More Information
Using a scale helps translate real distances into manageable measurements on maps. For every 4 cm on the map, you represent 20 km. This approach is essential for understanding how real-world distances correspond visually.
Tips
- Confusing the direction of the ratio: Ensure you multiply the correct way by using the scale to convert kilometers to centimeters.
- Forgetting to simplify units: Always make sure the units (e.g., cm with km) properly cancel out during calculations.
AI-generated content may contain errors. Please verify critical information
