calculate the coorsponding linear scale of the areal 1cm square to 100kmsquare
To calculate the corresponding linear scale of a 1 cm square to a 100 km square, we need to determine the ratio between the lengths of the sides of the two squares.
Step 1: Calculate the area of each square.
The area of the 1 cm square is calculated by multiplying the length of one side by itself: 1 cm * 1 cm = 1 cm².
The area of the 100 km square can be calculated in the same way: 100 km * 100 km = 10,000 km².
Step 2: Find the ratio of the areas.
Divide the area of the 100 km square by the area of the 1 cm square: 10,000 km² / 1 cm² = 10,000,000,000 cm²/km².
Step 3: Convert the ratio to a linear scale.
Since we want to calculate the linear scale of the 1 cm square, we need to find the length of one side of the 100 km square that corresponds to the 1 cm side length.
To do this, we need to take the square root of the ratio we calculated: √(10,000,000,000 cm²/km²) ≈ 100,000 cm/km.
Therefore, the corresponding linear scale of the 1 cm square to the 100 km square is approximately 100,000 cm/km.