Chapter 6.3, Problem 23PPS

To determine

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

Answer to Problem 23PPS

  $x=4,y=3$

Explanation of Solution

Given:

The given figure is:

Calculation:

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

Finding the values of x and y:

  $\begin{array}{l}3x+3y=21\\ 3x=21-3y\\ x=7-y\end{array}$

Also,

  $\begin{array}{l}2x+4y=6y+\frac{1}{2}x\\ 2\left(7-y\right)+4y=6y+\frac{1}{2}\left(7-y\right)\\ 14+2y=\frac{11}{2}y+\frac{7}{2}\\ 2y-\frac{11}{2}y=\frac{7}{2}-14\\ -\frac{7}{2}y=-\frac{21}{2}\\ y=3\end{array}$

Put $y=3$ in $x=7-y$ to find the value of x:

  $\begin{array}{l}x=7-y\\ x=7-3\\ x=4\end{array}$