To find the length of the building on the scale drawing, we first need to determine the scale of the drawing based on the height of the building.
The actual height of the building is 120 meters and it is represented by 15 centimeters on the scale drawing.
We can find the scale factor by comparing the actual height to the height on the drawing:
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Convert the actual height from meters to centimeters: \[ 120 \text{ meters} = 120 \times 100 = 12000 \text{ centimeters} \]
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Now we find the scale factor by dividing the actual height by the height on the drawing: \[ \text{Scale factor} = \frac{12000 \text{ cm}}{15 \text{ cm}} = 800 \]
This means that every 1 centimeter on the drawing represents 800 centimeters (or 8 meters) in reality.
Next, to find the length of the building on the scale drawing, we first convert the actual length from meters to centimeters:
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The actual length of the building is 90 meters: \[ 90 \text{ meters} = 90 \times 100 = 9000 \text{ centimeters} \]
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Now, use the scale factor to find the length on the scale drawing: \[ \text{Length on scale drawing} = \frac{9000 \text{ cm}}{800} = 11.25 \text{ cm} \]
Thus, the length of the building on the scale drawing is \( \boxed{11.25} \) centimeters.
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