https://file.aiquickdraw.com/mathbot/file/17267178789198by3s3hv.jpg

The problem in the image involves two scale drawings of a garden. The scale of the first drawing is given as 8 feet to 1 centimeter, and the second scale is 2 feet to 1 centimeter. We are asked to find the lengths of the base and height of the garden in the second scale drawing, given the dimensions of the base and height in the first scale drawing.

### Here's how to solve it:

1. **Given Data:**
   - The first scale is **8 ft = 1 cm**.
   - The second scale is **2 ft = 1 cm**.
   - The dimensions of the garden in the first scale drawing are **2.4 cm (base)** and **3.6 cm (height)**.

2. **Convert the first scale dimensions to real-world measurements**:
   - For the **base**:
     - \( 2.4 \, \text{cm} \times 8 \, \text{ft/cm} = 19.2 \, \text{ft} \)
   - For the **height**:
     - \( 3.6 \, \text{cm} \times 8 \, \text{ft/cm} = 28.8 \, \text{ft} \)

3. **Convert these real-world dimensions into the second scale**:
   - For the **base**:
     - \( \frac{19.2 \, \text{ft}}{2 \, \text{ft/cm}} = 9.6 \, \text{cm} \)
   - For the **height**:
     - \( \frac{28.8 \, \text{ft}}{2 \, \text{ft/cm}} = 14.4 \, \text{cm} \)

So, the correct dimensions for the second scale drawing are **9.6 cm and 14.4 cm**, corresponding to option **D**.

### Kamal's Mistake:
Kamal chose option A (0.6 cm and 0.9 cm), which could be due to confusion about the scaling factors or a misunderstanding of how to convert between the scales.

Would you like further details on any part of this solution or have any questions?

### Related Questions:
1. How do you convert between different scales in geometry?
2. What are the typical errors made when working with scale drawings?
3. How do you calculate real-world dimensions from a scaled diagram?
4. What other methods are there for scaling figures besides ratio-based conversion?
5. How do changes in scale affect area and volume calculations?

### Tip:
Always check whether you're scaling up or down, and use the correct scale factor for each conversion step to avoid mistakes like Kamal's.

The scale from a garden to this drawing is 8 ft to 1 cm. The scale from the same garden to another drawing is 2 ft to 1 cm. What are the lengths of the base and height of the garden in the other scale drawing?

Learn how to solve a scale drawing problem where the garden dimensions are provided at two different scales. Find the correct dimensions for the base and height using proportions and conversion. Suitable for students in Grades 6-8.

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