# The perimeter of a rectangle is 36 meters. The length of the rectangle is 4 meters longer than the width. What is the length and width of the rectangle?

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5
Dec 24, 2015

Length $11 m$ and width $7 m$. The step by step explanation on working is given below.

#### Explanation:

Perimeter of rectangle is given by the formula $P = 2 \left(l + w\right)$

From the information we use $P = 36$.
Also given length is 4m longer than width, so if $w$ is width then $l = w + 4$

Let us setup the equation as

$36 = 2 \left(l + w\right)$
$\frac{36}{2} = \frac{2}{2} \left(l + w\right)$

$18 = l + w$

We know $l = w + 4$ substituting this

$18 = w + 4 + w$

Simplifying further
$18 = 2 w + 4$
$18 - 4 = 2 w + 4 - 4$
$14 = 2 w$
$\frac{14}{2} = 2 \frac{w}{2}$
$7 = w$
$w = 7$
$l = w + 4$
$l = 7 + 4 = 11$
$l = 11$

Answer length = $11 m$ and width = $7 m$

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