# Find the polynomial that represents the perimeter of a rectangle that has a length of 3x-2 and width of x+4?

Apr 20, 2018

$\text{perimeter } = 8 x + 4$

#### Explanation:

$\text{ the perimeter of a rectangle is }$

• " perimeter "=2l+2w

$\text{where l is the length and w the width}$

$\text{here "l=3x-2" and } w = x + 4$

$\Rightarrow \text{perimeter "=2(3x-2)+2(x+4)larrcolor(blue)"distribute}$

color(white)(rArr"perimeter ")=6x-4+2x+8larrcolor(blue)"collect like terms"

$\textcolor{w h i t e}{\Rightarrow \text{perimeter }} = 8 x + 4$

Apr 20, 2018

Perimeter$= 8 x + 4$

#### Explanation:

Perimeter of a rectangle is given by the formula $2 \cdot \text{length"+2*"width}$.

Length$= \left(3 x - 2\right)$, width$= \left(x + 4\right)$

$2 \left(3 x - 2\right) + 2 \left(x + 4\right)$

$\Rightarrow \left(6 x - 4\right) + \left(2 x + 8\right)$

collecting (grouping) like terms:

$\Rightarrow 6 x + 2 x + 8 - 4$

$\Rightarrow 8 x + 4$