Chapter 5, Problem 2RP

To determine

Find the perimeter of $ABCD$ .

Answer to Problem 2RP

  $36unit$

Explanation of Solution

Given information:

  

  $\begin{array}{l}AB=2x+6\\ BC=8\\ CD=x+8\end{array}$

Calculation:

Consider the given parallelogram has opposite sides are congruent

Let solve for $x$ ,

  $\begin{array}{l}AB=CD\\ 2x+6=x+8\\ 2x-x=8-6\\ x=2\\ putx=2in2x+6andx+8,\\ AB=2\left(2\right)+6=10\\ CD=2+8=10\end{array}$

Now find perimeter,

  $\begin{array}{l}P=2\left(l+w\right)\\ P=2\left(10+8\right)\\ P=36\end{array}$

Hence, the perimeter of $ABCD$ is $36unit$