To find the diagonal of a box, we can use the formula for the diagonal \( d \) of a rectangular prism, which is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
We need to check each option to see if the diagonal is at least 41.5 inches.
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20 inches, 20 inches, 27 inches \[ d = \sqrt{20^2 + 20^2 + 27^2} = \sqrt{400 + 400 + 729} = \sqrt{1529} \approx 39.1 \text{ inches} \]
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21 inches, 24 inches, 26 inches \[ d = \sqrt{21^2 + 24^2 + 26^2} = \sqrt{441 + 576 + 676} = \sqrt{1693} \approx 41.2 \text{ inches} \]
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23 inches, 24 inches, 25 inches \[ d = \sqrt{23^2 + 24^2 + 25^2} = \sqrt{529 + 576 + 625} = \sqrt{1730} \approx 41.6 \text{ inches} \]
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20 inches, 21 inches, 26 inches \[ d = \sqrt{20^2 + 21^2 + 26^2} = \sqrt{400 + 441 + 676} = \sqrt{1517} \approx 38.9 \text{ inches} \]
Now, comparing our results:
- The first option gives a diagonal of approximately 39.1 inches (not sufficient).
- The second option gives a diagonal of approximately 41.2 inches (not sufficient).
- The third option gives a diagonal of approximately 41.6 inches (sufficient).
- The fourth option gives a diagonal of approximately 38.9 inches (not sufficient).
Thus, the only option that has a diagonal of at least 41.5 inches is:
23 inches, 24 inches, 25 inches.