To find the length of the diagonal segment \( BE \) of the rectangular prism, we can use the 3D distance formula, which is derived from the Pythagorean theorem:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( d \) is the diagonal length,
- \( l \) is the length of the prism,
- \( w \) is the width of the prism,
- \( h \) is the height of the prism.
Given:
- Length \( l = 32 \) cm
- Width \( w = 24 \) cm
- Height \( h = 44 \) cm
Now, we can plug in the values into the formula:
\[ d = \sqrt{(32)^2 + (24)^2 + (44)^2} \]
Calculating each square:
\[ (32)^2 = 1024 \] \[ (24)^2 = 576 \] \[ (44)^2 = 1936 \]
Adding these values together:
\[ d = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Now, calculating \( \sqrt{3536} \):
\[ \sqrt{3536} \approx 59.5 \text{ cm} \]
So, the length of the diagonal of the rectangular prism segment \( BE \) is approximately 59.5 cm, which matches one of the given options.
Final answer: 59.5 cm