Question
Use the image to answer the question.
A grid is shown with a rectangle drawn on it. The rectangle is 8 units long and 4 units wide, labeled with 8 and 4 respectively.
Scale: 1 box = 5 meters
Reproduce the scale drawing of a playground so that it has a scale of 1 box = 20 meters. Which drawing shows the new scale?
(1 point)
Responses
A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively. Scale: 1 box = 20 meters
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A grid is shown with a rectangle drawn on it. The rectangle is 8 units long and 4 units wide, labeled with 8 and 4 respectively.
Scale: 1 box = 5 meters
Reproduce the scale drawing of a playground so that it has a scale of 1 box = 20 meters. Which drawing shows the new scale?
(1 point)
Responses
A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 2 units long and 1 unit wide, labeled with 2 and 1 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 16 units long and 8 units wide, labeled with 16 and 8 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 6 units long and 3 units wide, labeled with 6 and 3 respectively. Scale: 1 box = 20 meters
A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively.
Scale: 1 box = 20 meters
Image with alt text: A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively. Scale: 1 box = 20 meters
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Answers
GPT-4o mini
To find the correct drawing that corresponds to the new scale of 1 box = 20 meters, we first need to calculate the dimensions of the rectangle in the new scale based on the original dimensions of 8 units long and 4 units wide with a scale of 1 box = 5 meters.
1. **Original dimensions**:
- Length: 8 units
- Width: 4 units
2. **Convert original dimensions to meters**:
- Length in meters = 8 units × 5 meters/unit = 40 meters
- Width in meters = 4 units × 5 meters/unit = 20 meters
3. **Convert to new dimensions** with the scale of 1 box = 20 meters:
- New Length in boxes = 40 meters ÷ 20 meters/box = 2 boxes
- New Width in boxes = 20 meters ÷ 20 meters/box = 1 box
In summary, with the new scale, the rectangle should be 2 units long and 1 unit wide.
Now, we check the provided options:
- **First Option**: 2 units long and 1 unit wide (Correct)
- **Second Option**: 16 units long and 8 units wide (Incorrect)
- **Third Option**: 6 units long and 3 units wide (Incorrect)
- **Fourth Option**: 3 units long and 2 units wide (Incorrect)
The correct drawing that shows the new scale (1 box = 20 meters) is the first option with the rectangle measuring 2 units long and 1 unit wide.
1. **Original dimensions**:
- Length: 8 units
- Width: 4 units
2. **Convert original dimensions to meters**:
- Length in meters = 8 units × 5 meters/unit = 40 meters
- Width in meters = 4 units × 5 meters/unit = 20 meters
3. **Convert to new dimensions** with the scale of 1 box = 20 meters:
- New Length in boxes = 40 meters ÷ 20 meters/box = 2 boxes
- New Width in boxes = 20 meters ÷ 20 meters/box = 1 box
In summary, with the new scale, the rectangle should be 2 units long and 1 unit wide.
Now, we check the provided options:
- **First Option**: 2 units long and 1 unit wide (Correct)
- **Second Option**: 16 units long and 8 units wide (Incorrect)
- **Third Option**: 6 units long and 3 units wide (Incorrect)
- **Fourth Option**: 3 units long and 2 units wide (Incorrect)
The correct drawing that shows the new scale (1 box = 20 meters) is the first option with the rectangle measuring 2 units long and 1 unit wide.