To determine the longest possible length and width of the rectangle with the appropriate level of precision, we need to analyze the given measurements and consider the level of precision for each dimension.
The length is labeled as 5.2 inches, which is precise to the nearest tenth, and the width is labeled as 3.8 inches, which is also precise to the nearest tenth. The longest possible length would be slightly above 5.2 inches, and the longest possible width would be slightly above 3.8 inches.
Now let's examine the response options:
- 3.95 and 5.35 - This suggests the width could be around 3.95 inches and the length 5.35 inches, which are both longer than the original numbers but do not maintain the same precision level.
- 3.3 and 4.7 inches - These numbers are shorter than both dimensions and do not represent the longest possible length and width.
- 3.85 and 5.25 inches - These values are close to the original dimensions while staying within the levels of precision; the width is slightly greater than 3.8 inches, and the length is slightly lower than 5.2 inches, which may not qualify as 'longest'.
- 3.8 and 5.2 inches - These values are the exact dimensions given in the problem and thus represent the measured length and width, but they may not consider the longest possible increments above these values.
Based on the reasoning above, while none of the options provide a technical "longest" increment, the option 3.85 and 5.25 inches would be the closest representation of longer dimensions while adhering to the precision levels indicated. However, it does represent values that are in line with the precision given (tenths).
Therefore, if forced to select one based on measuring above the original values, I'd choose:
3.85 and 5.25 inches.