Chapter 5.3, Problem 3WE

To determine

To find: x

Answer to Problem 3WE

  $x=4$

Explanation of Solution

Given:

The diagram:

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

$AB=5x-8$ And $EF=3x$

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)

Consider the triangle $△YCD$ .

Here, points E and F are the mid points of $\overline{YC}$ and $\overline{YD}$ .

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

  $EF=\frac{1}{2}CD$ ….. (2)

From (1) and (2),

  $AB=EF$

Substitute $AB=5x-8$ And $EF=3x$

  $\begin{array}{c}5x-8=3x\\ 5x-3x=8\\ 2x=8\\ x=4\end{array}$