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)
Responses
59.5 cm
59.5 cm
51.2 cm
51.2 cm
54.4 cm
54.4 cm
46.6 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
First, let's find the length of segment BH using the Pythagorean theorem:
BH^2 = 32^2 + 24^2
BH^2 = 1024 + 576
BH^2 = 1600
BH = √1600
BH = 40 cm
Now, let's find the length of segment BE using the Pythagorean theorem:
BE^2 = BH^2 + HE^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 approximately 59.5 cm.