Chapter 11.6, Problem 19CCR

To determine

Tocalculate : The expression for perimeter and the value of the perimeter at $x=5$ .

Answer to Problem 19CCR

  $9xm-m$

  $44m$

Explanation of Solution

Given information : An image of the polygon is given where the dimension of all the sides are mentioned in terms of a variable $x$ and $m$ .

Formula used : We know the perimeter of any shape is the sum of its side length.

Calculation : Find the expression of the perimeter.

1. Given diagram is

  

Now, we will add all side lengths to get the expression of the perimeter.

  $(3x-2)m+(x+1)m+xm+4xm$

Now, distribute and add the like terms.

  $\begin{array}{l}(3x-2)m+(x+1)m+xm+4xm\\ =3xm-2m+xm+m+xm+4xm\\ =3xm+xm+xm+4xm-2m+m\\ =9xm-m\end{array}$

2. Now, find the perimeter for $x=5$

Plug $x=5$ in $9xm-m$ we get,

  $\begin{array}{l}=9\times 5m-m\\ =45m-m\\ =44m\end{array}$