Chapter 6.3, Problem 20PPS

To determine

The value of x and y so that the given quadrilateral is a parallelogram.

Answer to Problem 20PPS

  $x=30,y=15.5$

Explanation of Solution

Given:

The given figure is:

Calculation:

A quadrilateral is a parallelogram if both pairs of its opposite sides are parallel.

Finding the values of x and y:

  $\begin{array}{l}\frac{1}{4}x=y-8\\ x=4y-32\end{array}$

Also,

  $\begin{array}{l}4x-8=8y-12\\ 4\left(4y-32\right)-8=8y-12\\ 16y-136=8y-12\\ 16y-8y=-12+136\\ 8y=124\\ y=15.5\end{array}$

Put $y=15.5$ in $x=4y-32$ to find the value of x:

  $\begin{array}{l}x=4y-32\\ x=4\left(15.5\right)-32\\ x=62-32\\ x=30\end{array}$