To find the length of the diagonal of the rectangular prism, segment \( BE \), we can use the 3D distance formula. The vertices of the rectangular prism can be represented in a 3D coordinate system as follows:
- Point B (0, 0, 0)
- Point E (length, width, height) = (32 cm, 24 cm, 44 cm)
The formula for the distance \( d \) between two points \( (x_1, y_1, z_1) \) and \( (x_2, y_2, z_2) \) in 3D space is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
Plugging in the coordinates for points B and E:
\[ (x_1, y_1, z_1) = (0, 0, 0) \quad \text{and} \quad (x_2, y_2, z_2) = (32, 24, 44) \]
The distance \( BE \) is:
\[ BE = \sqrt{(32 - 0)^2 + (24 - 0)^2 + (44 - 0)^2} \]
Calculating each term:
- \( (32 - 0)^2 = 32^2 = 1024 \)
- \( (24 - 0)^2 = 24^2 = 576 \)
- \( (44 - 0)^2 = 44^2 = 1936 \)
Adding these values:
\[ BE = \sqrt{1024 + 576 + 1936} = \sqrt{3536} \]
Now we compute \( \sqrt{3536} \):
\[ \sqrt{3536} \approx 59.5 \text{ cm} \quad \text{(to the nearest tenth)} \]
Thus, the length of the diagonal of the rectangular prism, segment \( BE \), is 59.5 cm.
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