We are given that 5 cm on the map represents 2.5 km of terrain. To find how many centimeters correspond to 15 km of terrain, we first determine the scale factor from the given information.

The ratio is:

$\frac{5 \, \text{cm}}{2.5 \, \text{km}}$

Now, we set up a proportion to find the number of centimeters ($x$) for 15 km:

$\frac{5 \, \text{cm}}{2.5 \, \text{km}} = \frac{x \, \text{cm}}{15 \, \text{km}}$

To solve for $x$, cross-multiply:

$5 \times 15 = 2.5 \times x$

$75 = 2.5x$

Now, divide both sides by 2.5:

$x = \frac{75}{2.5} = 30 \, \text{cm}$

So, 15 km of terrain would be represented by 30 cm on the map.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. If 10 cm on the map represents 5 km, how many cm would 20 km be?
2. What is the scale ratio of the map if 5 cm represents 2.5 km?
3. How many kilometers does 1 cm represent on the same map?
4. If 8 cm on the map represents 4 km, how much terrain does 32 cm represent?
5. How would you convert 12 km of terrain into cm on the map using the same scale?

Tip: When dealing with map scales, always set up a ratio or proportion to convert between map distances and real-world distances.