Chapter 4.2, Problem 50E

To determine

To find: the expression for perimeter of new polygon.

Answer to Problem 50E

The expression for perimeter of new polygon is $12x+16$ .

Explanation of Solution

Given information:

A rectangle is given as

  

Perimeter of new polygon is double of the given rectangle.

Calculation:

Expression for length and breadth of the original rectangle is given by

  $2x+3$ and $x+1$

So, perimeter of the rectangle is

  $\begin{array}{c}P=2\left[\left(2x+3\right)+\left(x+1\right)\right]\\ =2\left[2x+3+x+1\right]\\ =2\left[3x+4\right]\\ =6x+8\end{array}$

Now, perimeter of the new polygon is double of original rectangle.

  $\begin{array}{c}P\text{'}=2P\\ =2\left(6x+8\right)\\ =12x+16\end{array}$

Hence, expression for perimeter of new polygon is $12x+16$ .