The length of a rectangular 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 segment BE, we first need to find the length of segment HE.
Using the Pythagorean theorem in triangle HBH, we have:
HB^2 = BH^2 - HH^2
HB^2 = 40^2 - 24^2
HB^2 = 1600 - 576
HB^2 = 1024
HB = 32 cm
Now, we can find the length of segment HE using the Pythagorean theorem in triangle HEO where EO is the height of the rectangular prism:
HE^2 = HO^2 + EO^2
HE^2 = 32^2 + 44^2
HE^2 = 1024 + 1936
HE^2 = 2960
HE = √2960
HE ≈ 54.4 cm
Finally, we can find the length of segment BE in triangle BHE using the Pythagorean theorem:
BE^2 = BH^2 + HE^2
BE^2 = 40^2 + 54.4^2
BE^2 = 1600 + 2963.36
BE^2 = 4563.36
BE ≈ √4563.36
BE ≈ 67.6 cm
Therefore, the length of the diagonal of the rectangular prism, segment BE, is approximately 67.6 cm when rounded to the nearest tenth.