Jen measured a swimming pool and made a scale drawing. In real life, the pool is 40 meters long. It is 8 millimeters long in the drawing. What scale factor does the drawing use?

Question

Simplify your answer and write it as a fraction.
Jen measured a swimming pool and made a scale drawing. In real life, the pool is 40 meters long. It is 8 millimeters long in the drawing. What scale factor does the drawing use?

Simplify your answer and write it as a fraction.

Answer 1

To find the scale factor of the drawing, we need to compare the length of the swimming pool in real life to the length of the pool in the drawing.

1. Convert the real-life length of the pool from meters to millimeters: \[ 1 \text{ meter} = 1000 \text{ millimeters} \] Therefore, \[ 40 \text{ meters} = 40 \times 1000 = 40000 \text{ millimeters} \]

2. Now we have the real-life length of the pool (40000 mm) and the length in the drawing (8 mm).

3. The scale factor is found by dividing the drawing length by the real-life length: \[ \text{Scale Factor} = \frac{\text{Drawing Length}}{\text{Real Length}} = \frac{8 \text{ mm}}{40000 \text{ mm}} \]

4. Simplify the fraction: \[ \text{Scale Factor} = \frac{8}{40000} = \frac{1}{5000} \]

So the scale factor that the drawing uses is: \[ \frac{1}{5000} \]