To find the length of the diagonal of a rectangular prism, we can use the following formula for the diagonal \(d\):
\[ d = \sqrt{l^2 + w^2 + h^2} \]
where:
- \(l\) = length,
- \(w\) = width,
- \(h\) = height.
Given:
- \(l = 32 , \text{cm}\)
- \(w = 24 , \text{cm}\)
- \(h = 44 , \text{cm}\)
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 add these values together:
\[ d = \sqrt{1024 + 576 + 1936} \] \[ d = \sqrt{3536} \]
Now, we calculate the square root:
\[ d \approx 59.5 , \text{cm} \]
Thus, the length of the diagonal \(BE\) of the rectangular prism is approximately \(59.5 , \text{cm}\).
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