Bot GPT 4-o mini To find the correct scaling of the playground drawing, we first need to convert the dimensions of the rectangle from the original scale (1 box = 5 meters) to the new scale (1 box = 20 meters).
The original rectangle measures:
- Length: 8 units
- Width: 4 units
Using the original scale:
- Length in meters: \(8 \text{ units} \times 5 \text{ meters/unit} = 40 \text{ meters}\)
- Width in meters: \(4 \text{ units} \times 5 \text{ meters/unit} = 20 \text{ meters}\)
Now we convert these dimensions to the new scale (1 box = 20 meters):
- For the length: \(40 \text{ meters} \div 20 \text{ meters/unit} = 2 \text{ units}\)
- For the width: \(20 \text{ meters} \div 20 \text{ meters/unit} = 1 \text{ unit}\)
So the new dimensions of the rectangle on the scaled grid should be:
- Length: 2 units
- Width: 1 unit
Now, we can check the responses:
- 16 units long and 8 units wide: This is incorrect, as it implies a larger rectangle than the original.
- 2 units long and 1 unit wide: This matches our calculation, so this is likely correct.
- 6 units long and 3 units wide: This is incorrect, as it also implies a larger rectangle.
- 3 units long and 2 units wide: This is incorrect, as it suggests a different proportion than originally scaled.
Therefore, the correct drawing that represents the new scale is the rectangle that is 2 units long and 1 unit wide.
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