Question

Suppose you have a map that uses the scale 1 cm to 200 m. You draw a new map of the same place using the scale 1 cm to 20 m. How does your new map compare to your original map? How does the length change? How does the area change?

Answer 1

Switching from a map scale of 1 cm to 200 m to a new scale of 1 cm to 20 m will result in the new map being larger, with lengths 10 times longer and areas 100 times larger compared to the original map.

Step-by-step explanation:

When switching from a scale of 1 cm to 200 m to a new scale of 1 cm to 20 m for a map, the new map will be larger compared to the original map. With the new scale, every 1 cm on the map represents a shorter distance of 20 meters in reality, which means that the same area will take up more space on the map. To find out how much the length and area change, we need to understand the difference in scale factors.

The original scale has a scale factor of 1:200 (1 cm on the map represents 200 meters in reality), while the new scale has a scale factor of 1:20. Therefore, the new scale is 10 times larger than the original scale (since 200/20 equals 10). This implies that lengths on the new map will be 10 times longer than on the original map. For the area, since area is a two-dimensional measurement, we square the change in the scale factor to determine the change in area. That means the area on the new map will be 102, or 100 times larger than on the original map.