Question

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?

Answer 1

`"length"=35 " feet"` and `"width"=10" feet"`

Explanation:

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

`color(blue)(2xx"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

`color(red)("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 `"width"`.

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

Distribute the `2` through

`8xx"width"-10+2xx"width"=90`

Combine your term's with `"width"`

`10xx"width"-10=90`

Add `10` to both sides.

`10xx"width"=100`

Divide both sides by `10`

`color(green)("width"=10)`

Now you can plug `"width"` into your original equation for length above. Recall:

`color(red)("length" = 4xx"width"-5)`
`color(red)("length" = 4xxcolor(green)(10)-5)`
`"length"=40-5`
`"length"=35`

ANSWER: `"length"=35 " feet"` and `"width"=10" feet"`