A rectangular room has a length of 18 ft and a width of 11 1/2 ft. On an architectural scale drawing of this room, the length is 9 cm. What is the width of the room on the drawing?

To solve this problem, we need to determine the width of the room on the drawing given the length and its scaled length.

First, let's calculate the scaling factor used in the architectural drawing. The actual length of the room is 18 feet, and the length on the drawing is 9 cm.

We can set up the following ratio to find the scale factor:

\[
\text{Scale factor} = \frac{\text{Length on drawing}}{\text{Actual length}} = \frac{9 \text{ cm}}{18 \text{ ft}}
\]

Simplifying this ratio, we get:

\[
\text{Scale factor} = \frac{9}{18} = \frac{1}{2} \text{ cm per foot}
\]

Next, we need to find the width of the room on the drawing using this scale factor. The actual width of the room is 11.5 feet.

Using the scale factor:

\[
\text{Width on drawing} = \text{Actual width} \times \text{Scale factor}
\]

\[
\text{Width on drawing} = 11.5 \text{ ft} \times \frac{1}{2} \text{ cm per foot}
\]

\[
\text{Width on drawing} = 11.5 \times 0.5 = 5.75 \text{ cm}
\]

So, the width of the room on the drawing is 5.75 cm.

Would you like more details or have any questions about this solution?

Here are 5 questions you might consider asking next:
1. How do you convert between different units of measurement in scaling problems?
2. Can you explain how to calculate area or perimeter using scaled dimensions?
3. What are some common scales used in architectural drawings and their applications?
4. How do you handle scaling in different types of geometric shapes?
5. Can you provide examples of how scaling is used in map reading and model building?

**Tip:** When working with scale drawings, always ensure the units are consistent and accurately converted to maintain the correct proportions.

Learn how to solve a scale drawing problem where the length of a room is scaled down on an architectural drawing. This problem involves calculating the width of the room on the drawing using a given scale factor. Suitable for students in Grades 6-8.

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