page
E
D
F
G
diagonal
H
height
C
A
width
length
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.
(1 point)
59.5 cm
○ 46.6 cm
54.4 cm
○ 51.2 cm
To find the length of the diagonal of the rectangular prism, segment BE, we need to use the Pythagorean theorem twice.
First, we need to find the length of segment EF (the diagonal of the base). Using the Pythagorean theorem on triangle EBF:
EF^2 = EB^2 + BF^2
40^2 = EB^2 + 24^2
1600 = EB^2 + 576
EB^2 = 1024
EB = √1024
EB = 32 cm
Next, we need to find the length of segment BE (the diagonal of the rectangular prism) using the Pythagorean theorem on triangle BEH:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 44^2
BE^2 = 1600 + 1936
BE^2 = 3536
BE = √3536
BE = 59.5 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is 59.5 cm. Rounded to the nearest tenth, the answer is 59.5 cm.