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Bot GPT 4-o mini To solve the problem, we need to determine the dimensions of the rectangle when the scale changes from 1 box = 4 centimeters to 1 box = 2 centimeters.
The original rectangle is 6 units long and 2 units wide. In the original scale:
- Length in centimeters = 6 units * 4 cm/unit = 24 cm
- Width in centimeters = 2 units * 4 cm/unit = 8 cm
Now, when we change the scale to 1 box = 2 centimeters, we need to find out how many boxes (or units) the rectangle will occupy in the new scale but keeping the dimensions proportional in terms of the original rectangle's size.
To find the new scaled dimensions, we divide the original dimensions (in centimeters) by the new scale factor to find their size in the new boxes:
- New length in boxes = 24 cm / 2 cm/box = 12 boxes
- New width in boxes = 8 cm / 2 cm/box = 4 boxes
Thus, the rectangle should be represented as being 12 units long and 4 units wide when the scale is 1 box = 2 centimeters.
Based on the options provided, the correct answer is:
**A grid is shown with a rectangle drawn on it. The rectangle is 12 units long and 4 units wide, labeled with 12 and 4 respectively. Scale: 1 box = 2 centimeters.**