## Sunday, June 15, 2014

### Rectangular Parallelepiped Problem, 11

Category: Solid Geometry, Plane Geometry

"Published in Vacaville, California, USA"

If a, b, and c are the sides of a rectangular parallelepiped, find the length of its diagonal.

Solution:

To illustrate the problem, it is better to draw the figure as follows

 Photo by Math Principles in Everyday Life

The first thing that we need to do is to consider the lower base of the above figure first and then solve for the length of the diagonal by using Pythagorean Theorem.

 Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the length of a diagonal of the lower base is

Since all sides as well as the faces of a rectangular parallelepiped are perpendicular to each other, then it follows that x is perpendicular to c.

 Photo by Math Principles in Everyday Life

Therefore, by Pythagorean Theorem, the length of a diagonal of a rectangular parallelepiped is

The diagonal of a rectangular parallelepiped is a length or a distance between the opposite vertices. You can draw four diagonals in a rectangular parallelepiped.