https://file.aiquickdraw.com/mathbot/file/172969794818344hfq6im.jpg

To solve this problem, we need to determine the scale factor the builder used when creating the scale drawing of the playground.

### Step 1: Write down the given information
- **Scale drawing dimensions:**
  - Length = 8.6 cm
  - Width = 15 cm
- **Actual playground dimensions:**
  - Actual length = 21.5 feet
  - Actual width = 37.5 feet

### Step 2: Calculate the scale factor for each dimension
We need to calculate how much the actual dimensions were scaled down in the drawing. To do that, we compare the corresponding lengths and widths between the actual playground and the scale drawing. But first, we need to convert the actual playground dimensions to centimeters, since the scale drawing is in centimeters.

1 foot = 30.48 cm (conversion factor)

- **Convert the actual length:**
  \[
  21.5 \text{ feet} \times 30.48 \frac{\text{cm}}{\text{foot}} = 654.32 \text{ cm}
  \]

- **Convert the actual width:**
  \[
  37.5 \text{ feet} \times 30.48 \frac{\text{cm}}{\text{foot}} = 1143 \text{ cm}
  \]

### Step 3: Calculate the scale factor for both dimensions
Now, divide the actual dimensions by the dimensions of the scale drawing:

- **For the length:**
  \[
  \text{Scale factor for length} = \frac{654.32 \text{ cm}}{8.6 \text{ cm}} \approx 76.08
  \]

- **For the width:**
  \[
  \text{Scale factor for width} = \frac{1143 \text{ cm}}{15 \text{ cm}} \approx 76.2
  \]

### Step 4: Conclusion
The scale factor used for the drawing is approximately the same for both the length and width, around **76**.

### Final Answer:
1 cm = 76 feet (rounded).

Would you like more details on any part of this solution, or do you have any questions?

Here are 5 related questions to further explore this topic:
1. How would the solution change if the drawing had different units, like inches instead of centimeters?
2. What would the scale factor be if the dimensions of the playground were in meters instead of feet?
3. Can you find the area of the actual playground and compare it to the area of the drawing?
4. What is the importance of maintaining the same scale factor for both length and width in a scale drawing?
5. How could you determine the scale factor if only one dimension (length or width) was given?

**Tip:** When dealing with scale drawings, ensure all units are consistent before calculating the scale factor.

A builder creates a scale drawing of a playground, where the length is 8.6 cm and the width is 15 cm. If the actual length of the playground is 21.5 feet and the actual width is 37.5 feet, what scale factor did the builder use to create the scale drawing? 1 cm = ______

Learn how to calculate the scale factor for a playground drawing, given the dimensions in both centimeters and feet. This problem involves unit conversion from feet to centimeters and solving ratios for scale. Suitable for Grades 6-8.

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