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
46.6 cm
46.6 cm
51.2 cm
51.2 cm
54.4 cm
To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Let's consider triangle BEH. We have the height (BH) as 40 cm, the width (BE) as 24 cm, and the length (EH) as 44 cm (which is the height of the prism).
Using the Pythagorean theorem, we can find the length of BE (the diagonal of the rectangular prism):
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 approximately 59.5 cm.
The closest answer choice is 59.5 cm.