The length of the diagonal \( d \) of a square can be calculated using the formula:
\[ d = s \sqrt{2} \]
where \( s \) is the length of one side of the square.
If the diagonal measures 7 inches to the nearest whole number, the actual length of the diagonal could be in the range of:
\[ 6.5 \text{ inches} \leq d < 7.5 \text{ inches} \]
We can find the corresponding range for the side length \( s \) by rearranging the formula for the diagonal:
\[ s = \frac{d}{\sqrt{2}} \]
Calculating the side length for the extremes of the diagonal range:
- For \( d = 6.5 \):
\[ s = \frac{6.5}{\sqrt{2}} \approx \frac{6.5}{1.414} \approx 4.6 \text{ inches} \]
- For \( d = 7.5 \):
\[ s = \frac{7.5}{\sqrt{2}} \approx \frac{7.5}{1.414} \approx 5.3 \text{ inches} \]
Thus, the side length \( s \) could be in the range of:
\[ 4.6 \text{ inches} \leq s < 5.3 \text{ inches} \]
Now we check the diagonal length for \( s \):
- If \( s \) is 4.6 inches, then:
\[ d \approx 4.6 \sqrt{2} \approx 6.5 \text{ inches} \]
- If \( s \) is 5.3 inches, then:
\[ d \approx 5.3 \sqrt{2} \approx 7.5 \text{ inches} \]
In conclusion, the actual length of the diagonal of the square could be in the range of approximately 6.5 inches to 7.5 inches. Therefore, it could be any number in this interval.
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