To convert the scale of the drawer to 1 box = 6 inches, we need to first determine the actual dimensions of the drawer in inches based on the current scale.
Given that the current dimensions of the drawer are:
- Width \( W = 8 \) boxes
- Height \( H = 4 \) boxes
Now, converting boxes to inches using the new scale:
- Width in inches = \( 8 \) boxes × \( 6 \) inches/box = \( 48 \) inches
- Height in inches = \( 4 \) boxes × \( 6 \) inches/box = \( 24 \) inches
Next, we need to convert those dimensions back to boxes using the new scale (1 box = 6 inches).
To find the length in boxes of the new scale drawing:
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For the width in boxes: \[ \text{Width in boxes} = \frac{48 \text{ inches}}{6 \text{ inches/box}} = 8 \text{ boxes} \]
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For the height in boxes: \[ \text{Height in boxes} = \frac{24 \text{ inches}}{6 \text{ inches/box}} = 4 \text{ boxes} \]
Thus, the dimensions in the new scale drawing will remain the same, so the length in boxes of the new scale drawing remains 8 boxes and the height remains 4 boxes.
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