To find the actual length of the living space based on the scale provided, we can use the following relationship:
- From the given scale, 2 centimeters in the drawing corresponds to 2.5 meters in reality.
Now, we can find the number of actual meters represented by the length in the drawing:
\[ \text{Scale Ratio} = \frac{2.5 \text{ meters}}{2 \text{ centimeters}} = 1.25 \text{ meters per centimeter} \]
Next, we can multiply the length of the living space in centimeters by the scale factor to find the actual length:
\[ \text{Actual Length} = \text{Length in centimeters} \times \text{Scale Ratio} \]
Substituting the values:
\[ \text{Actual Length} = 16.8 \text{ cm} \times 1.25 \text{ m/cm} \]
\[ \text{Actual Length} = 21 \text{ meters} \]
Therefore, the actual length of the living space is 21 meters.