Answer: The dimensions are: "length = 58 ft. and width = 26 ft." ;
or; write as: " 58 ft. × 26 ft. " .
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Explanation:
To solve:
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Note:
The formula for the perimeter of a rectangle:
P = 2L + 2w ;
in which:
"P = perimeter;
"L = length ;
"w = width ;
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The dimensions are the "Length" {"L"] by the width {"w"} ; or; " L × w " ;
Given:
L = 6 + 2w ;
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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.") !!!
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Let us check our answer:
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!
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Hope this answer—and explanation—is of help to you.
Best wishes in your academic endeavors—and within the "Brainly" community!
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