To find the length of the diagonal of the rectangular prism, we can use the three-dimensional distance formula. The formula for the diagonal \( d \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given:
- Length \( l = 32 \) cm
- Width \( w = 24 \) cm
- Height \( h = 44 \) cm
We can substitute these values into the formula:
\[ d = \sqrt{32^2 + 24^2 + 44^2} \]
Calculating each square:
- \( 32^2 = 1024 \)
- \( 24^2 = 576 \)
- \( 44^2 = 1936 \)
Now we can sum these values:
\[ d = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Calculating \( \sqrt{3536} \):
\[ \sqrt{3536} \approx 59.5 \text{ cm (rounded to one decimal place)} \]
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 59.5 cm.