Question

Jen made a scale drawing of a petting zoo. In real life, the goat pen is 8 meters long. It is 2 centimeters long in the drawing. What scale factor does the drawing use?

Simplify your answer and write it as a ratio, using a colon.

Answer 1

To determine the scale factor of Jen's drawing, we need to compare the real-life length of the goat pen to its length in the drawing.

- Real-life length of the goat pen: 8 meters
- Length of the goat pen in the drawing: 2 centimeters

First, we need to convert the real-life measurement to the same unit as the drawing. Since the drawing's length is in centimeters, we will convert 8 meters to centimeters:

\[
8 \text{ meters} = 8 \times 100 \text{ centimeters} = 800 \text{ centimeters}
\]

Next, we set up the ratio of the real-life measurement to the drawing measurement:

\[
\text{Scale Factor} = \frac{\text{Real Life Length}}{\text{Drawing Length}} = \frac{800 \text{ cm}}{2 \text{ cm}}
\]

Now, we simplify the ratio:

\[
\frac{800}{2} = 400
\]

Thus, the scale factor is \(400:1\).

So the final answer as a ratio is:

\[
\boxed{400:1}
\]