# The length of a rectangular piece of steel in a bridge is 2 meters less than triple the width. The perimeter of the piece of steel is 36 meters. How do you find the length of the piece of steel?

Oct 4, 2015

Length of the Steel piece is $\text{13 m}$

#### Explanation:

Let the width be equal to $w$ meters. The length is $2$ meters less than triple the width. So the length of the steel piece is

$l = 3 w - 2$

Now the perimeter of a rectangle is given by

$P = 2 \cdot \left(l + w\right) \text{ }$, where

$l$ is the length
$w$ is the width.

In this case, the perimeter will be

$P = 2 \cdot \left({\underbrace{3 w - 2}}_{\textcolor{b l u e}{= l}} + w\right)$

$P = 2 \cdot \left(4 w - 2\right) = \text{36 m} \to$ given

So

$2 \cdot \left(4 w - 2\right) = 36$

$4 w - 2 = \frac{36}{2} = 18$

$4 w = 18 + 2 = 20 \implies w = \frac{20}{4} = \text{5 m}$

The length is

$l = 3 \cdot 5 - 2 = \text{13 m}$