To solve this problem, we can use a proportion based on the scale between the actual height of the building and its height in the drawing.

We know:

• Actual height of the building: 125 meters
• Height of the building in the drawing: 25 cm
• Actual length of the building: 80 meters
• Length in the drawing: unknown (let's call it x)

We set up a proportion between the height and length:

$\frac{\text{Height of building in the drawing}}{\text{Actual height of the building}} = \frac{\text{Length of building in the drawing}}{\text{Actual length of the building}}$

$\frac{25 \, \text{cm}}{125 \, \text{m}} = \frac{x \, \text{cm}}{80 \, \text{m}}$

First, let's convert the height of the building to the same units (centimeters), knowing that 1 meter = 100 centimeters:

$\frac{25 \, \text{cm}}{12500 \, \text{cm}} = \frac{x}{8000 \, \text{cm}}$

Now, cross-multiply to solve for x:

$25 \times 8000 = x \times 12500$

$200000 = 12500x$

$x = \frac{200000}{12500} = 16 \, \text{cm}$

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

Would you like more details or have any questions?

Here are some related questions:

1. How would the scale change if the drawing height were 30 cm instead of 25 cm?
2. What is the scale ratio of the drawing?
3. If the length of the building were 100 meters, what would the length be on the drawing?
4. How would you calculate the area of the building in the drawing?
5. How could you use this method to determine the scale for other dimensions?

Tip: Always make sure units are consistent when solving proportional problems.