To find the length of the diagonal of the rectangular prism, segment BE, we can use the Pythagorean theorem.
Let's label the length of segment BE as x. We can form a right triangle with segment BC, segment BH, and segment HC. Since segment BH is the diagonal of the base, it forms a right angle with segment BC and HC.
Using the Pythagorean theorem, we have:
BC^2 + HC^2 = BH^2
Substituting in the given values, we have:
24^2 + 44^2 = 40^2
576 + 1936 = 1600
2512 = 1600
Now, we can find the length of segment HC by subtracting the heights of segments BH and BC:
HC = 44 - 32
HC = 12
Now, we can solve for BC:
BC^2 + 12^2 = 40^2
BC^2 + 144 = 1600
BC^2 = 1456
BC ≈ 38.1
Finally, we can find the length of segment BE by using the Pythagorean theorem again:
BE^2 = BC^2 + BH^2
BE^2 = 38.1^2 + 40^2
BE^2 ≈ 1453.61 + 1600
BE^2 ≈ 3053.61
BE ≈ √3053.61
BE ≈ 55.3
Rounding to the nearest tenth, the length of the diagonal of the rectangular prism, segment BE, is approximately 55.3 cm.
So the correct answer is not in the given options.