To find the length of the diagonal of the rectangular prism, segment \( BE \), we can use the three-dimensional distance formula, which is based on the Pythagorean theorem. The formula for the length of the diagonal \( d \) in a rectangular prism is:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 32 \) cm,
- Width \( w = 24 \) cm,
- Height \( h = 44 \) cm.
Now substituting 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 summing these values:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Next, we find \( \sqrt{3536} \):
Calculating it gives approximately:
\[ d \approx 59.5 \text{ cm} \]
Therefore, the length of the diagonal \( BE \) of the rectangular prism is approximately 59.5 cm.
Thus, the answer is:
59.5 cm