The corresponding linear scale for an area scale of 1cm² to 2km² is found by taking the square root of the area ratio, giving a linear scale of 1cm to 0.02km, after converting from centimeters to kilometers.
The corresponding linear scale for an area scale of 1cm² to 2km² can be determined by equating the scale factor in terms of area to the scale factor in terms of length. Since area is a two-dimensional measure (length x width), the square root is taken to find the linear scale.
To convert the area scale to a linear scale, the following steps can be followed:
- Recognize that 1cm² on the map represents 2km² in reality.
- Understand that 1km is equivalent to 1000 meters, thus 2km² is (2000 meters) x (2000 meters) = 4 x 10^6 m².
- Since 1cm² equals 4 x 10^6 m², then 1cm² is equivalent to 4 x 10^6 cm² (as 1m² is 10,000cm²).
- To find the linear scale, take the square root of the area scale: √(4 x 10^6) cm = 2000 cm.
- Convert the linear scale in centimeters back to kilometers: 2000 cm = 20 meters = 0.02 km.
Therefore, the linear scale that corresponds to the area scale of 1cm² to 2km² is 1cm to 0.02km.