# The perimeter of a rectangular wooden deck is 90 feet. The deck's length, I, is 5 feet less than 4 times its width, w. Which System of linear equations can be used to determine the dimensions, n feet, of the wooden deck?

May 28, 2017

$\text{length"=35 " feet}$ and $\text{width"=10" feet}$

#### Explanation:

You are given the perimeter of the rectangular deck is $90$ feet.

$\textcolor{b l u e}{2 \times \text{length"+2xx"width} = 90}$

You are also given that the deck's length is $5$ feet less than $4$ times it's width. That is

$\textcolor{red}{\text{length" = 4xx"width} - 5}$

Those two equations are your system of linear equations. The second equation can be plugged into the first equation. This gives us an equation entirely in terms of $\text{width}$.

color(blue)(2xx(color(red)(4xx"width"-5))+2xx"width"=90)

Distribute the $2$ through

$8 \times \text{width"-10+2xx"width} = 90$

Combine your term's with $\text{width}$

$10 \times \text{width} - 10 = 90$

Add $10$ to both sides.

$10 \times \text{width} = 100$

Divide both sides by $10$

$\textcolor{g r e e n}{\text{width} = 10}$

Now you can plug $\text{width}$ into your original equation for length above. Recall:

$\textcolor{red}{\text{length" = 4xx"width} - 5}$
$\textcolor{red}{\text{length} = 4 \times \textcolor{g r e e n}{10} - 5}$
$\text{length} = 40 - 5$
$\text{length} = 35$

ANSWER: $\text{length"=35 " feet}$ and $\text{width"=10" feet}$