Consider a right tetrahedron, that is, a tetrahedron that has a vertex R whose three adj...

Consider a right tetrahedron, that is, a tetrahedron that has a vertex R whose three adjacent faces are pairwise perpendicular. (See Figure 1.119.) Use the result of Exercise 27 to show the following three-dimensional analogue of the Pythagorean theorem: If a, b, and c denote the areas of the three faces adjacent to R and d denotes the area of the face opposite R, then a² + b² + c² = d².