To find the length of the diagonal of the rectangular prism (segment \( BE \)), we can use the 3D distance formula. The diagonal \( BE \), which goes from vertex \( B \) at coordinates \( (0, 0, 0) \) to vertex \( E \) at coordinates \( (l, w, h) \), can be calculated using the dimensions of the prism.
Given:
- Length \( l = 32 , \text{cm} \)
- Width \( w = 24 , \text{cm} \)
- Height \( h = 44 , \text{cm} \)
The coordinates for the points are:
- \( B(0, 0, 0) \)
- \( E(32, 24, 44) \)
Using the 3D distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
Substituting the coordinates of points \( B \) and \( E \):
\[ d = \sqrt{(32 - 0)^2 + (24 - 0)^2 + (44 - 0)^2} \] \[ d = \sqrt{32^2 + 24^2 + 44^2} \] Calculating each square: \[ 32^2 = 1024 \] \[ 24^2 = 576 \] \[ 44^2 = 1936 \] Now, summing these values: \[ d = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Calculating the square root: \[ d \approx 59.5 , \text{cm} , \text{(rounded to the nearest tenth)} \]
Therefore, the length of the diagonal \( BE \) rounded to the nearest tenth is:
59.5 cm.