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 given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.
From the information provided:
- Length \( (l) = 32 , \text{cm} \)
- Width \( (w) = 24 , \text{cm} \)
- Height \( (h) = 44 , \text{cm} \)
Now we can 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:
\[ d = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Next, we calculate \( \sqrt{3536} \):
Calculating the square root:
\[ \sqrt{3536} \approx 59.5 \]
Thus, the length of the diagonal of the rectangular prism segment \( BE \) rounded to the nearest tenth is:
\[ \boxed{59.5 , \text{cm}} \]