To find the length of the diagonal of the rectangular prism, \( BE \), we can use the 3-dimensional distance formula. The formula for the diagonal \( d \) of a rectangular prism is given by:
\[ d = \sqrt{(length)^2 + (width)^2 + (height)^2} \]
Given the dimensions of the prism:
- Length = 32 cm
- Width = 24 cm
- Height = 44 cm
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, we sum these values:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Now we calculate \( \sqrt{3536} \):
\[ \sqrt{3536} \approx 59.5 \text{ cm} \]
Rounding to the nearest tenth, the length of the diagonal \( BE \) is approximately \( 59.5 \text{ cm} \).
So the correct response is:
59.5 cm