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 diagonal segment BE, we first need to calculate the length of side segment BE.
To do this, we can use the Pythagorean theorem in triangle BEH:
BE^2 = BH^2 + EH^2
BE^2 = 40^2 + 24^2
BE^2 = 1600 + 576
BE^2 = 2176
BE = sqrt(2176)
BE ≈ 46.6 cm
Now, we can find the length of the diagonal segment BE in the rectangular prism by using the Pythagorean theorem again in triangle BEC:
BE^2 = BC^2 + EC^2
46.6^2 = 32^2 + 44^2
46.6^2 = 1024 + 1936
46.6^2 = 2960
BE = sqrt(2960)
BE ≈ 54.4 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 54.4 cm.