To find the length of the diagonal of the rectangular prism, segment \( BE \), we can use the formula for the diagonal \( d \) of a rectangular prism with dimensions length \( l \), width \( w \), and height \( h \):
\[ d = \sqrt{l^2 + w^2 + h^2} \]
Given:
- \( l = 32 , \text{cm} \)
- \( w = 24 , \text{cm} \)
- \( h = 44 , \text{cm} \)
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:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Next, we need to calculate \( \sqrt{3536} \):
\[ \sqrt{3536} \approx 59.5 \]
Thus, the diagonal length of the rectangular prism, segment \( BE \), is approximately \( 59.5 , \text{cm} \).
The correct answer is:
59.5 cm