Final answer:
To calculate the distance represented by 5 cm on the map, a proportion using the scale of 8 cm to 5 km is set up and solved, resulting in 3.125 kilometers as the actual distance for 5 cm on the map.
Step-by-step explanation:
The question asks to calculate the actual distance in kilometers that corresponds to 5 centimeters on a map, given that the scale is 8 cm for 5 km. To find the answer, we need to set up a proportion because the scale of the map is a ratio that helps us to convert distances on the map to real-world distances.
First, we write the given scale ratio as 8 cm / 5 km. Then, we write a proportion with the new map distance of 5 cm on one side and the unknown real distance in kilometers on the other side:
8 cm / 5 km = 5 cm / x km
Now, we solve for x by cross-multiplying and dividing:
8x = 5 * 5
x = 25 / 8
x = 3.125 km
Therefore, 5 centimeters on the map represents an actual distance of 3.125 kilometers.