To find the length of the diagonal of the rectangular prism, segment BE, we can use the three-dimensional distance formula. The diagonal \( BE \) can be calculated with the following formula:
\[ BE = \sqrt{l^2 + w^2 + h^2} \]
Where:
- \( l \) 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 these values:
\[ BE = \sqrt{32^2 + 24^2 + 44^2} \]
Calculating each square:
\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]
Adding these together:
\[ BE = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Now we calculate \( \sqrt{3536} \):
\[ BE \approx 59.5 \text{ cm} \]
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.