To find the length of the diagonal of the rectangular prism (segment BE), we use the formula for the diagonal \(d\) of a rectangular prism given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(l\) is the length,
- \(w\) is the width, and
- \(h\) is the height.
Given:
- \(l = 32 , \text{cm}\)
- \(w = 24 , \text{cm}\)
- \(h = 44 , \text{cm}\)
Now, substitute these 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, add these values together:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Now, calculating the square root:
\[ d \approx 59.5 , \text{cm} \]
Thus, rounding to the nearest tenth, the length of the diagonal of the rectangular prism (segment BE) is approximately:
\[ \boxed{59.5 , \text{cm}} \]