Chapter 5.3, Problem 4WE

To determine

To find: x

Answer to Problem 4WE

  $x=2$

Explanation of Solution

Given:

The diagram:

Points A, B, E and F are the mid points of $\overline{XC}$ , $\overline{XD}$ , $\overline{YC}$ and $\overline{YD}$ .

$CD=8x$ And $AB=3x+2$

Consider the figure shown below:

Consider the triangle $△XCD$ .

Here, points A and B are the mid points of $\overline{XC}$ and $\overline{XD}$ .

So, by theorem 5-11 part (2), the side $\overline{AB}$ is half as long as the third side $\overline{CD}$ .

$AB=\frac{1}{2}CD$ ….. (1)

Substitute $CD=8x$ and $AB=3x+2$

  $\begin{array}{c}AB=\frac{1}{2}CD\\ 3x+2=\frac{1}{2}\left(8x\right)\\ 3x+2=4x\end{array}$

  $\begin{array}{c}2=4x-3x\\ 2=x\end{array}$