   Chapter 9.1, Problem 49E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A diagonal of a cube joins two vertices so that the remaining points of the diagonal lie in the interior of the cube. Show the diagonal of the cube having edges of length e is e √ 3 units long.

To determine

The diagonal of the cube having edges of length e is e3 units long.

Explanation

Given,

The edge of the cube = e units.

The diagonal of a right rectangular prism with dimensions l, w, and h is given by,

d=l2+w2+h2

Substitute; l=e, w=e, and h=e. in the above formula as all the edges of cube are same in length,

d=l2+w

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