The length of a rectangular room is 6 feet longer than twice the width. if the room perimeter is 168 feet, what are the room's dimensions,?

The dimensions are: "length = 58 ft. and width = 26 ft." ;

or; write as: " 58 ft. × 26 ft. " .

Explanation:

To solve:

Note:

The formula for the perimeter of a rectangle:

P = 2L + 2w ;

in which:

"P = perimeter;

"L = length ;

"w = width ;

The dimensions are the "Length" {"L"] by the width {"w"} ; or; " L × w " ;

Given:

L = 6 + 2w ;

P = 2L + 2w ;

Plug in: "168" (given) for "P".

and: "(6 + 2w)" for "L" ;

to solve for: "w" {the "width"} ;

→ P = 2L + 2w ;

→ 168 = 2(6 + 2w) + 2w ;

Factor out a "2" in the "right hand side" of the equation:

→ 168 = 2 [(6 + 2w) + (w)]

Divide each side o the equation by "2" ;

→ 168 / 2 = { 2 [(6 + 2w) + (w)] } / 2 ;

to get:

→ 84 = [(6 + 2w) + (w)] ;

Note: Simplify the "right-hand side" of the equation:

→ [(6 + 2w) + (w)] = 6 + 2w + 1w = 6 + 3w ;

and rewrite the equation:

→ 84 = 6 + 3w ;

↔ 3w + 6 = 84 ;

Subtract "6" from each side of the equation:

→ 3w + 6 − 6 = 84 − 6 ;

to get:

→ 3w = 78 ;

Divide each side of the equation by "3" ;

to isolate "w" on one side of the equation; & to solve for "w" [the "width"] ;

→ 3w / 3 = 78 / 2 ;

to get:

→ w = 26.

Now:

Given: " L = 6 + 2w " ;

Solve for: "L" .

Plug in "26" for "w" in the equation; to solve for "L" :

→ " L = 6 + 2w ;

→ " L = 6 + 2(26) ;

→ " L = 6 + 52 ;

→ " L = 58 " .

So, we have: " L = 58 ft. " ; and "w = 26 ft."

So the dimensions are: "length = 58 ft. and width = 26 ft." ;

or; write as: " 58 ft. × 26 ft. " .

→ Do not forget the units of "feet" (abbreviated "ft.") !!!

Let us check our

Use the formula:

P = 2L + 2w ;

→ When "P = 168" ; (as given in the problem); does the equation hold true when "L = 58" and when "w = 26" ??

Let us check! ;

→ 168 =? 2(58) + 2(26) ??

→ 168 =? 116 + 52 ??

→ 168 =? 168 ??

→ 168 = 168 !! Yes!

Hope this answer—and explanation—is of help to you.

Best wishes in your academic endeavors—and within the community!

the answer is c.

for continuous functions, they continue in the same pattern and you have to find that pattern kinda like slope

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.