To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean Theorem. Since triangle BHE is a right triangle, we can use the lengths of BH and HE to find the length of BE.
BH, the length of the diagonal of the base, is given as 40 cm. And since BE is an extension of BH, it is also equal to 40 cm.
To find HE, we can use the lengths of the sides of the rectangular prism that are perpendicular to HE. HE is perpendicular to both BC (width) and CD (height). So, we can use the Pythagorean theorem to find HE.
BC (width) is given as 24 cm, and CD (height) is given as 44 cm.
Using the Pythagorean Theorem, we have:
HE^2 = BC^2 + CD^2
HE^2 = 24^2 + 44^2
HE^2 = 576 + 1936
HE^2 = 2512
Taking the square root of both sides, we find:
HE ≈ √2512
HE ≈ 50.1 cm
Finally, we can use the lengths of BH and HE to find the length of BE using the Pythagorean Theorem:
BE^2 = BH^2 + HE^2
BE^2 = 40^2 + 50.1^2
BE^2 = 1600 + 2510.01
BE^2 ≈ 4110.01
Taking the square root of both sides, we find:
BE ≈ √4110.01
BE ≈ 64.1 cm
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism, segment BE, is approximately 64.1 cm. Therefore, the correct answer is 64.1 cm.