# A rectangular room is 6 meters longer than it is wide, and its perimeter is 32 meters. How do you find the dimension of the room?

Sep 5, 2015

Length is 11 m.; Width is 5 m.

#### Explanation:

Define:
color(white)("XX")L = " length"
color(white)("XX")W = " width"

Given
$\textcolor{w h i t e}{\text{XX}} L = W + 6$
color(white)("XX")"(perimeter = " = 2(L+W) = 32

$\textcolor{w h i t e}{\text{XX}} \rightarrow 2 \left(\left(W + 6\right) + W\right) = 32$

$\textcolor{w h i t e}{\text{XX}} \rightarrow 2 W + 6 = 16$

$\textcolor{w h i t e}{\text{XX}} \rightarrow W = 5$

and since $L = W + 6$
$\textcolor{w h i t e}{\text{XX}} \rightarrow L = 11$

Sep 5, 2015

5m x 11m

#### Explanation:

take the width of the room as $x$, then the length of the room becomes $x + 6$ according to the data.

i can take these data and write an equation as follows which shows the perimeter of the room

$32 = 2 \left(x + 6\right) + 2 x$
$32 = 4 x + 12$
$4 x = 20$
$x = 5 m$ this is the width of the room

the length of the room = $5 + 6 = 11 m$

so the dimensions of the room :
5m x 11m