Cara drew a scale drawing of an apartment. A rug by the door, which is 3 feet wide in real life, is 6 inches wide in the drawing. What is the drawing's scale factor?

Question

Simplify your answer and write it as a fraction.

Answer 1

To find the scale factor of Cara's drawing, we need to compare the dimensions in the drawing to the actual dimensions of the rug.

1. Convert the actual width of the rug to inches: \[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \]

2. Determine the width of the rug in the drawing: The width is given as 6 inches.

3. Calculate the scale factor: The scale factor is the ratio of the size in the drawing to the actual size: \[ \text{Scale Factor} = \frac{\text{Width in drawing}}{\text{Actual width}} = \frac{6 \text{ inches}}{36 \text{ inches}} \]

4. Simplify the fraction: \[ \frac{6}{36} = \frac{1}{6} \]

Thus, the scale factor of the drawing is \(\boxed{\frac{1}{6}}\).