To find the length of the diagonal of the rectangular prism (segment BE), we can use the 3D distance formula. The formula for the diagonal \( d \) of a rectangular prism with dimensions length \( l \), width \( w \), and height \( h \) is:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given:
- Length \( l = 32 , \text{cm} \)
- Width \( w = 24 , \text{cm} \)
- Height \( h = 44 , \text{cm} \)
Now we can calculate the diagonal:
\[ d = \sqrt{(32)^2 + (24)^2 + (44)^2} \]
Calculating each term:
\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]
Adding these together:
\[ 1024 + 576 + 1936 = 3536 \]
Now take the square root:
\[ d = \sqrt{3536} \approx 59.5 , \text{cm} \]
Therefore, the length of the diagonal of the rectangular prism (segment BE) is approximately 59.5 cm (rounded to the nearest tenth).
The answer is 59.5 cm.