   Chapter 9.1, Problem 47E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# 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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