# The perimeter of a rectangular carpet is 54ft. The lenght is 3ft greater than the width. How do you find the length and width?

Sep 5, 2015

Length is 15 feet; Width is 12 feet

#### Explanation:

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

$P = 2 \left(L + W\right) = 54$
$\textcolor{w h i t e}{\text{XX}} \rightarrow L + W = 27$

$L = W + 3$
$\textcolor{w h i t e}{\text{XX}} \rightarrow \left(W + 3\right) + W = 27$

$\textcolor{w h i t e}{\text{XX}} \rightarrow 2 W = 24$

$\textcolor{w h i t e}{\text{XX}} \rightarrow W = 12$

and since $L = W + 3$
$\textcolor{w h i t e}{\text{XX}} L = 15$