To find the length of the diagonal of the rectangular prism, we can use the formula for the space diagonal of a rectangular prism:
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \( l \) is the length of the prism,
- \( w \) is the width of the prism,
- \( h \) is the height of the prism.
Given:
- Length \( l = 32 , \text{cm} \)
- Width \( w = 24 , \text{cm} \)
- Height \( h = 44 , \text{cm} \)
Let's calculate the diagonal:
\[ d = \sqrt{32^2 + 24^2 + 44^2} \]
Calculating each term:
\[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \]
Now, sum these values:
\[ 1024 + 576 + 1936 = 3536 \]
Now, take the square root of 3536:
\[ d = \sqrt{3536} \approx 59.5 , \text{cm} \]
Therefore, the length of the diagonal of the rectangular prism, segment \( BE \), is approximately \( 59.5 , \text{cm} \).
Final answer: 59.5 cm
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