To find out the new dimensions of the playground when scaling from a scale where one box equals 5 meters to a new scale where one box equals 20 meters, we first need to understand the relationship between the two scales.
- Original Scale: 1 box = 5 meters
- New Scale: 1 box = 20 meters
Since the new scale is 4 times larger than the original scale (20 meters / 5 meters = 4), we will effectively need to multiply the dimensions of the playground by 4.
From your question, it looks like the original dimensions of the playground are 8 inches long and 4 inches high (as inferred from the dimensions of the box).
Calculating the new dimensions:
- Length: 8 inches × 4 = 32 inches
- Height: 4 inches × 4 = 16 inches
Now, looking at the options provided:
A) 3 inches long, 2 inches high
B) 2 inches long, 1 inch high
C) 16 inches long, 8 inches high
D) 6 inches long, 3 inches high
None of these options match exactly the calculated 32 inches long and 16 inches high, which means the right option should reflect those dimensions on the new scale of 20 meters.
However, if we consider an effective conversion to the given options and their relative scaling:
- Scale down from 32-inch length and 16-inch height in a proportional way to the new scale of 20m could logically lead you to match their proportions.
Therefore, if any of these lengths were provided as inputs to represent a similar scale down effect, you would choose accordingly. With no exact matches, it's possible we have to select based on proportions given.
If a choice reflecting a similar dimension or aspect ratio were needed, then Option C: 16 inches long and 8 inches high has a similar proportion of 2:1, which reflects a scaling approach matching original proportions before consideration of a fixed ground measurement.
If you can clarify the dimensions explicitly desired, that can help confirm if one of these options can match or represent key dimensions to scale back to playground sizes as required.
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