To find the length of the diagonal of the rectangular prism (segment BE), we can use the three-dimensional distance formula. The formula for the diagonal \(d\) of a rectangular prism is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(l\) is the length,
- \(w\) is the width,
- \(h\) is the height.
Given values:
- Length (\(l\)) = 32 cm
- Width (\(w\)) = 24 cm
- Height (\(h\)) = 44 cm
Now plugging in these values:
\[ d = \sqrt{(32)^2 + (24)^2 + (44)^2} \]
Calculating each square:
\[ (32)^2 = 1024 \] \[ (24)^2 = 576 \] \[ (44)^2 = 1936 \]
Now sum these values:
\[ d = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Now calculating the square root:
\[ d \approx 59.5 \text{ cm} \]
Thus, the length of the diagonal of the rectangular prism, segment BE, rounded to the nearest tenth is 59.5 cm.