To find the length of the diagonal of the rectangular prism (segment BE), we can use the formula for the diagonal of a rectangular prism:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height, and
- \(d\) is the diagonal.
Given:
- Length (\(l\)) = 32 cm,
- Width (\(w\)) = 24 cm,
- Height (\(h\)) = 44 cm.
Let's plug 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, adding these values together:
\[ 1024 + 576 + 1936 = 3536 \]
Now, we find the square root:
\[ d = \sqrt{3536} \]
Calculating the square root:
\[ d \approx 59.5 , \text{cm} \]
So, rounding to the nearest tenth, the length of the diagonal of the rectangular prism (segment BE) is:
\[ \boxed{59.5 , \text{cm}} \]