To find the length of the diagonal of the rectangular prism (segment BE), we can use the Pythagorean Theorem.
The length of the base (segment AB) is given as 32 cm, the width (segment BC) is given as 24 cm, and the diagonal of the base (segment BH) is given as 40 cm.
We can see that triangle ABH is a right triangle, with segment AB and segment BH as its legs.
Using the Pythagorean Theorem, we have:
AB^2 + BH^2 = BE^2
Substituting the given values:
32^2 + 40^2 = BE^2
1024 + 1600 = BE^2
2624 = BE^2
Taking the square root of both sides to solve for BE:
BE ≈ √2624
BE ≈ 51.2 cm (rounded to the nearest tenth)
Therefore, the correct answer is 51.2 cm.