The cuboid's space diagonals all have the same length. If the edge lengths of a cuboid are a, b, and c, then the distinct rectangular faces have edges (a, b), (a, c), and (b, c); so the respective face diagonals have lengths   and
Given that all space diagonals of a cuboid are congruent, we can express this as a relationship among its edge lengths. Specifically, for a cuboid with edge lengths a, b, and c, the distinct rectangular faces have edges (a, b), (a, c), and (b, c); so the respective face diagonals have lengths √(a² + b²) and √(a² + c²).