Chapter 12.2, Problem 8CE

To determine

To find: The numerical value of $XM$ .

Answer to Problem 8CE

The length of $XM$ is equal to $3\sqrt{3}$ .

Explanation of Solution

Given information: The given figure is as follows.

  

Calculation:

Consider the triangle $XYZ$ of the given figure. Each edge of pyramid $XYZ$ is equal to $6$ .

The length of $XM$ can be determined by using Pythagoras Theorem in triangle $XMY$ as:

  $\begin{array}{c}X{M}^2+M{Y}^2=X{Y}^2\\ X{M}^2=X{Y}^2-M{Y}^2\\ XM=\sqrt{X{Y}^2-M{Y}^2}\end{array}$

Further simplify.

  $\begin{array}{c}XM=\sqrt{6^2-3^2}\\ =\sqrt{36-9}\\ =3\sqrt{3}\end{array}$

Therefore, the length of $XM$ is equal to $3\sqrt{3}$ .