E
D
F
diagonal
G
height
H
C
A
length
width
B
The length of the prism is 32 cm, the width is 24 cm, the height is 44 cm, and the length of the diagonal of the base, segment BH, is 40 cm. Find the length of the diagonal of the rectangular prism, segment BE. Round the answer to the nearest tenth.
To find the length of the diagonal BE, we first need to calculate the length of segment EH using the Pythagorean theorem.
EH^2 = BH^2 + BE^2
EH^2 = 24^2 + 32^2
EH^2 = 576 + 1024
EH^2 = 1600
EH = √1600
EH = 40 cm
Now, we can find the length of diagonal BE using EH and the height of the prism.
BE^2 = EH^2 + height^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
BE = √3536
BE ≈ 59.4 cm
Therefore, the length of the diagonal BE is approximately 59.4 cm.