To determine whether a box's diagonal meets the required minimum of 41.5 inches, we can use the formula for the diagonal \( d \) of a rectangular box (also known as a rectangular prism):
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
We'll calculate the diagonal for each option:
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21 inches, 24 inches, 26 inches: \[ d = \sqrt{21^2 + 24^2 + 26^2} = \sqrt{441 + 576 + 676} = \sqrt{1693} \approx 41.2 \text{ inches} \] (Does not meet requirement)
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23 inches, 24 inches, 25 inches: \[ d = \sqrt{23^2 + 24^2 + 25^2} = \sqrt{529 + 576 + 625} = \sqrt{1730} \approx 41.6 \text{ inches} \] (Meets requirement)
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20 inches, 21 inches, 26 inches: \[ d = \sqrt{20^2 + 21^2 + 26^2} = \sqrt{400 + 441 + 676} = \sqrt{1517} \approx 38.0 \text{ inches} \] (Does not meet requirement)
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20 inches, 20 inches, 27 inches: \[ d = \sqrt{20^2 + 20^2 + 27^2} = \sqrt{400 + 400 + 729} = \sqrt{1529} \approx 39.1 \text{ inches} \] (Does not meet requirement)
From these calculations, the only option that has a diagonal of at least 41.5 inches is:
23 inches, 24 inches, 25 inches