Chapter 1.3, Problem 39WE

To determine

To find: the value of z and then find $GE$ and $EH$ and to state whether E is the midpoint

of $\overline{GH}$ or not.

Answer to Problem 39WE

  $\begin{array}{l}Z=8,\\ GE=10\\ EH=10\end{array}$

Explanation of Solution

Given information:

The given information is as follows.

  $GE=z+2,GH=20,EH=2z-6$

Calculation:

Find the value of z.

  $\begin{array}{l}GE+EH=GH\\ z+2+2z-6=20\\ 3z=20+6-2\\ 3z=24\\ z=8\end{array}$

Then,

  $\begin{array}{l}GE=8+2=10\\ EH=2(8)-6=10\end{array}$

Hence, E is the midpoint of $\overline{GH}$ or not.