To find the length of the diagonal of the rectangular prism (segment BE), we can use the 3D diagonal formula for a rectangular prism. The formula for the length of the diagonal \(d\) is:
\[ d = \sqrt{L^2 + W^2 + H^2} \]
where \(L\) is the length, \(W\) is the width, and \(H\) is the height.
Given:
- Length \(L = 32 , \text{cm}\)
- Width \(W = 24 , \text{cm}\)
- Height \(H = 44 , \text{cm}\)
Now, we can substitute the values into the formula:
\[ d = \sqrt{32^2 + 24^2 + 44^2} \]
Calculating each term:
\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]
Now, summing these values:
\[ 1024 + 576 + 1936 = 3536 \]
Now take the square root:
\[ d = \sqrt{3536} \approx 59.5 , \text{cm} \]
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism (segment BE) is approximately:
\[ \boxed{59.5 , \text{cm}} \]
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