Layla drew a scale drawing of a house. The scale she used was 10 centimeters = 5 meters. What scale factor does the drawing use?

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
12 hours ago

To find the scale factor, we start with the given scale of 10 centimeters representing 5 meters.

First, we convert the measurements to the same unit. We can convert 5 meters to centimeters:

\[
5 \text{ meters} = 5 \times 100 \text{ cm} = 500 \text{ cm}
\]

Now we have:

- 10 cm (in the drawing) corresponds to 500 cm (in real life).

Next, we can express this as a ratio:

\[
\text{Scale} = \frac{\text{Drawing size}}{\text{Real size}} = \frac{10 \text{ cm}}{500 \text{ cm}}
\]

We simplify the fraction:

\[
\frac{10}{500} = \frac{1}{50}
\]

This means for every 1 cm in the drawing, it represents 50 cm in reality.

To express the scale factor as a ratio, we write it as:

\[
1:50
\]

Thus, the scale factor used in Layla's drawing is \( \boxed{1:50} \).