Ian drew a scale drawing of an office. The desk is 3 inches long in the drawing. The actual desk is 6 feet long. What scale factor does the drawing use?

Question

Simplify your answer and write it as a fraction.

Answer 1

To find the scale factor used in Ian's drawing, we begin by converting the actual length of the desk from feet to inches since the scale drawing is measured in inches.

1. Convert the actual desk length to inches: \[ 6 \text{ feet} = 6 \times 12 \text{ inches} = 72 \text{ inches} \]

2. Determine the scale factor: The scale factor is the ratio of the length in the drawing to the actual length: \[ \text{Scale Factor} = \frac{\text{Length in Drawing}}{\text{Actual Length}} = \frac{3 \text{ inches}}{72 \text{ inches}} \]

3. Simplify the fraction: \[ \frac{3}{72} = \frac{1}{24} \]

Thus, the scale factor that Ian used in the drawing is: \[ \boxed{\frac{1}{24}} \]