Chapter 5.3, Problem 14WE

To determine

To find: The values of x and y .

Answer to Problem 14WE

The length of x and y are $10\text{units}$ and $5\text{units}$ respectively.

Explanation of Solution

Given:

The parallel lines are shown below:

  

AE , BF , CG and DH are parallel to each other and EF = FG = GH . Length of BC and CD are $2x-y$ and $x+y$ respectively. Length of AB is 15 units.

Calculation:

Here, ADHE is the trapezoid as AE is parallel to DH .

As EF = FG = GH and AE , BF , CG and DH are parallel to each other then the lines BF and CG are the midsegment of the trapezoid.

Hence,

  $AB=BC=CD$

The length BC is,

  $\begin{array}{l}BC=AB\\ 2x-y=15\mathrm{......}\left(1\right)\end{array}$

The length CD is,

  $\begin{array}{l}CD=AB\\ x+y=15\mathrm{......}\left(2\right)\end{array}$

Solve the equations (1) and (2) as follows:

  $\begin{array}{l}\underset{\_}{\begin{array}{l}x+y=15\\ 2x-y=15\end{array}}\\ 3x=30\\ x=10\end{array}$

Substitute 10 for x in equation (2) as follows:

  $\begin{array}{c}10+y=15\\ y=5\end{array}$

Thus, the length of x and y are $10\text{units}$ and $5\text{units}$ respectively.