To find the length of the diagonal \( BE \) of the rectangular prism, we can use the formula for the diagonal \( d \) of a rectangular prism given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
From the information provided:
- Length \( l = 32 \) cm
- Width \( w = 24 \) cm
- Height \( h = 44 \) cm
Now we will 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, summing these values:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Now, we can compute the square root of \( 3536 \):
\[ d \approx 59.5 \text{ cm} \]
Thus, the length of the diagonal \( BE \) of the rectangular prism is approximately \( 59.5 \) cm. Rounding to the nearest tenth, we get:
\[ \text{The answer is } 59.5 \text{ cm.} \]