To determine the scale factor of the drawing, we can set up a ratio comparing the length of the living room in the drawing to the actual length of the living room in real life.

Given:

• Length of the living room in the drawing: 6 cm
• Actual length of the living room: 10 m

We need to make sure both measurements are in the same units before setting up the ratio. Let's convert 10 meters to centimeters: $10 \, \text{m} = 10 \times 100 = 1000 \, \text{cm}$

Now, the ratio of the length in the drawing to the actual length is: $\frac{6 \, \text{cm}}{1000 \, \text{cm}} = \frac{6}{1000}$

Simplifying the fraction: $\frac{6}{1000} = \frac{3}{500}$

Thus, the scale factor is $\frac{3}{500}$.

Would you like further details or have any questions?

Here are 5 questions to explore:

1. How would the scale factor change if the actual living room were 20 meters long?
2. What would be the length of the living room in the drawing if the scale factor was $\frac{1}{200}$?
3. How can you use the scale factor to find other dimensions in the apartment?
4. If a different room was 5 meters long in real life, how long would it be in the drawing?
5. How do scale factors relate to map-making and architecture?

Tip: Always ensure that both measurements are in the same units when calculating scale factors.