To find the length of the diagonal of the rectangular prism, segment B E, we can use the Pythagorean theorem.
First, we find the length of the diagonal of the base in terms of the length, width, and height of the prism. Let's call the length of segment B E x.
From the right triangle formed by segments B H, H E, and B E, we have:
(B H)^2 + (H E)^2 = (B E)^2
Substitute the known values:
(40)^2 + (24)^2 = x^2
1600 + 576 = x^2
2176 = x^2
Take the square root of both sides to find x:
x = √2176
x ≈ 46.6
Therefore, the length of the diagonal of the rectangular prism, segment B E, is approximately 46.6 cm.