Chapter 12.2, Problem 7CE

To determine

To find: The numerical value of $VC$ .

Answer to Problem 7CE

The length of $VC$ is equal to $\sqrt{136}$ .

Explanation of Solution

Given information: The given figure is as follows.

  

Calculation:

The edge length of square base is equal to $12$ , and the height of pyramid is equal to $8$ .

The length of $VC$ can be determined by using Pythagoras theorem in triangle $VOC$ .

The length of $OC$ can be calculated as:

  $\begin{array}{c}OC=\sqrt{O{M}^2+M{C}^2}\\ =\sqrt{6^2+6^2}\\ =\sqrt{36+36}\\ =6\sqrt{2}\end{array}$

In triangle $VOC$ , the length of $VC$ is

  $\begin{array}{c}VC=\sqrt{O{C}^2+V{O}^2}\\ =\sqrt{{\left(6\sqrt{2}\right)}^2+8^2}\\ =\sqrt{72+64}\\ =\sqrt{136}\end{array}$

Therefore, the length of $VC$ is equal to $\sqrt{136}$ .