# The length of a rectangle is 12 cm more than 6 times the width The perimeter is 108cm. How do you find length and width?

Jun 29, 2016

Breadth = 6cm and length =48cm

#### Explanation:

In word problems where you want an equation, you need to define the unknown quantities first. It helps to choose the smaller quantity as $x$ and write the other quantities in terms of $x$.

Let the breadth of the rectangle be $x$.
6 times the breadth is $6 x$.
The length is 12cm longer than $6 x$
The length is $6 x + 12$

The perimeter of 108cm is made of 4 sides all added together, 2 lengths and 2 breadths. Write this..

$x + x + \left(6 x + 12\right) + \left(6 x + 12\right) = 108 \text{ now solve for } x$

$14 x + 24 = 108$
$14 x = 84$

$x = 6$

$x = 6$ is the breadth and $6 x + 12 = 36 + 12 = 48$ is the length,

Check:
$6 + 6 + 48 + 48 = 108$cm