Bot GPT 4-o mini To find the length of the diagonal 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, and \( h \) is the height of the prism.
Given:
- Length \( l = 32 \) cm
- Width \( w = 24 \) cm
- Height \( h = 44 \) cm
Now, we can calculate the diagonal \( d \):
\[ d = \sqrt{(32)^2 + (24)^2 + (44)^2} \]
Calculating the squares:
\[ (32)^2 = 1024 \] \[ (24)^2 = 576 \] \[ (44)^2 = 1936 \]
Now, summing these:
\[ d = \sqrt{1024 + 576 + 1936} \]
Calculating the total:
\[ 1024 + 576 + 1936 = 3536 \]
Now, we take the square root:
\[ d = \sqrt{3536} \]
Calculating the square root gives approximately:
\[ d \approx 59.5 \text{ cm} \]
Therefore, the length of the diagonal of the rectangular prism, segment \( BE \), is approximately 59.5 cm.
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