To find the length of the diagonal of the rectangular prism, we can use the formula for the diagonal \(d\) of a rectangular prism, which is given by:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(l\) is the length of the prism,
- \(w\) is the width of the prism,
- \(h\) is the height of the prism.
In this case:
- \(l = 32 \text{ cm}\)
- \(w = 24 \text{ cm}\)
- \(h = 44 \text{ cm}\)
Now we can substitute the values into the formula:
\[ d = \sqrt{32^2 + 24^2 + 44^2} \]
Calculating the squares:
\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]
Now, adding these values together:
\[ 1024 + 576 + 1936 = 3536 \]
Now, take the square root:
\[ d = \sqrt{3536} \]
Calculating the square root:
\[ d \approx 59.5 \text{ cm} \]
So, the length of the diagonal of the rectangular prism \(BE\) is approximately \(59.5 \text{ cm}\) when rounded to the nearest tenth.
The correct answer is 59.5 cm.