https://file.aiquickdraw.com/mathbot/file/1726780987103qzp79508.jpg

Let's go over the math problem from the image you uploaded.

1. **Write the scale as a ratio:**
   The scale given is \(1 \, \text{in.} = 10 \, \text{ft.}\), so the ratio is:
   \[
   \frac{1 \, \text{in.}}{10 \, \text{ft.}} = 1:10
   \]

2. **Write the ratio of the garden's actual length to its length in the drawing:**
   Let \(x\) represent the actual length of the garden. The drawing shows the garden's length as \(0.75 \, \text{in.}\). The ratio is:
   \[
   \frac{x}{0.75 \, \text{in.}}
   \]

3. **Use the ratios to write a proportion:**
   Now, you can set up a proportion using the scale:
   \[
   \frac{1 \, \text{in.}}{10 \, \text{ft.}} = \frac{0.75 \, \text{in.}}{x}
   \]

4. **Solve the proportion:**
   Cross-multiply to find \(x\):
   \[
   x = 0.75 \times 10 = 7.5 \, \text{ft.}
   \]

5. **The actual length of the garden:**
   From the calculation, the actual length of the garden is \(7.5 \, \text{ft.}\).

6. **For the park's problem:**
   The scale is \(0.5 \, \text{in.} = 10 \, \text{ft.}\), and the park is \(4.5 \, \text{in.}\) long in the drawing.
   Using the same method:
   \[
   \frac{0.5 \, \text{in.}}{10 \, \text{ft.}} = \frac{4.5 \, \text{in.}}{x}
   \]
   Cross-multiply:
   \[
   x = \frac{4.5 \times 10}{0.5} = 90 \, \text{ft.}
   \]
   So, the actual length of the park is \(90 \, \text{ft.}\).

Would you like further clarifications or details on any step?

Here are 5 follow-up questions to consider:
1. How can you use a scale to calculate area rather than just length?
2. What is the significance of cross-multiplication in solving proportions?
3. Can you think of real-life applications of scale drawings?
4. How would the calculation change if the scale was \(1 \, \text{cm} = 5 \, \text{m}\)?
5. What is the relationship between scales and similar figures in geometry?

**Tip:** When solving proportions, always check if the units in the ratio are consistent before starting calculations.

What is the actual length of the garden based on the scale 1 inch = 10 feet, and the garden's drawing length is 0.75 inches?

Learn how to solve a scale drawing problem involving a garden with a scale of 1 inch = 10 feet. This math solution guides you step-by-step through solving proportions, cross-multiplying, and finding the actual length of a garden in feet.

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