AHSME 1993 Problem 29

Which of the following could NOT be the lengths of the external diagonals of a right regular prism [a "box"]? (An $\textit{external diagonal}$ is a diagonal of one of the rectangular faces of the box.) $\text{(A) }\{4,5,6\} \text{(B) } \{4,5,7\} \text{(C) } \{4,6,7\} \text{(D) } \{5,6,7\} \text{(E) } \{5,7,8\}$