To find the length of the diagonal of the rectangular prism (segment BE), 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,
- \(h\) is the height.
In this case:
- Length \(l = 32 , \text{cm}\)
- Width \(w = 24 , \text{cm}\)
- Height \(h = 44 , \text{cm}\)
Substituting these values into the formula:
\[ D = \sqrt{32^2 + 24^2 + 44^2} \] \[ = \sqrt{1024 + 576 + 1936} \] \[ = \sqrt{3536} \]
Now, we calculate the square root:
\[ D \approx 59.5 , \text{cm} \]
Thus, the length of the diagonal of the rectangular prism (segment BE) is approximately 59.5 cm.
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