# The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

Dec 21, 2015

length$= 10.5$ $c m$
width$= 7.5$ $c m$

#### Explanation:

Start by making let statements to represent variables as the length and width as stated in the question.

Let $4 x$ represent the width.
Let $4 x + 3$ represent the length.

$2 \left[\left(4 x\right) + \left(4 x + 3\right)\right] = 36$
$2 \left[8 x + 3\right] = 36$
$8 x + 3 = 18$
$8 x = 15$
$x = \frac{15}{8}$

To find the dimensions, substitute $x = \frac{15}{8}$ into $4 x$ (width) and $4 x + 3$ (length).

Finding the width

$w = 4 x$

$w = 4 \left(\frac{15}{8}\right)$

$w = \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \left(\frac{15}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} ^ 2\right)$

$w = \frac{15}{2}$

$w = 7.5$

Finding the length

$l = 4 x + 3$

$l = 4 \left(\frac{15}{8}\right) + 3$

$l = \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} \left(\frac{15}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}} ^ 2\right) + 3$

$l = \frac{15}{2} + 3$

$l = \frac{21}{2}$

$l = 10.5$

$\therefore$, the length is $10.5$ $c m$ and the width is $7.5$ $c m$.