We can solve this problem by setting up a proportion based on the given information.

The actual height of the building is 125 meters, and the height on the scale drawing is 25 cm. The ratio of the scale drawing to the actual building is:

$\frac{\text{Height on drawing}}{\text{Actual height}} = \frac{25 \, \text{cm}}{125 \, \text{m}} = \frac{25 \, \text{cm}}{12500 \, \text{cm}} = \frac{1}{500}$

This tells us that every 1 cm on the drawing represents 500 cm in real life.

Now, we can use the same scale to find the length of the building on the scale drawing. The actual length of the building is 80 meters, which is 8000 cm.

Using the scale ratio:

$\frac{1}{500} = \frac{\text{Length on drawing}}{8000 \, \text{cm}}$

Solving for the length on the drawing:

$\text{Length on drawing} = \frac{8000}{500} = 16 \, \text{cm}$

Thus, the length of the building on the scale drawing is 16 cm.

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Do you want any further details or have any questions?

Here are 5 related questions for you to explore:

1. If the height on the drawing was 30 cm, what would the actual height of the building be?
2. What would the scale be if the height on the drawing was 20 cm?
3. How would you convert a length of 100 meters into the scale drawing using the same scale?
4. What is the total area of the building in square meters, and how would that translate to the scale drawing?
5. How would the proportions change if the drawing were to be scaled at 1:100?

Tip: Always ensure units are consistent when working with scale drawings.