The answer is:Â Â "25 feet"Â
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Explanation:
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Perimeter  = 2*(length) + 2*(width);Â
or; Â "P = 2L + 2w " ;.
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In this case: Â
"P = (2L + 2w) − 2 ⅚ " ; solve for "P" ; all units are in "feet (ft)" ;
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From the diagram; we are given:
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 L = 12 ¼ ;
Â
 w = 10 ;Â
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     →   " P = { [2* (12 ¼) ] + [2* 10] }  − 2 ⅚  " ;  Solve for "P" ;
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Note:  Rewrite "12 ¼" ;  AND:  "2 ⅚" as "improper fractions" :
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→ " 12 ¼ = [ (4*12) + 1 ] / 4 =Â
![\frac{48+1}{4}](/tpl/images/0075/2141/41846.png)
=Â
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
" Â ;
→ " 2 â…š  = [ (6*2) + 5 ] / 6 =Â
![\frac{12+5}{6}](/tpl/images/0075/2141/6ec2e.png)
=Â
![\frac{17}{6}](/tpl/images/0075/2141/0b52f.png)
" Â ;
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Rewrite our equation:Â
→  " P = { [2* (12 ¼) ] + [2* 10] }  − 2 ⅚  " ;;
substituting the "mixed numbers" with "improper fractions" ;
→  " P = { [2* (
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
) + [2* 10] }  −
![\frac{17}{6}](/tpl/images/0075/2141/0b52f.png)
 " ;
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→ Note: " 2*
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
;
          =Â
![\frac{2}{1}](/tpl/images/0075/2141/40438.png)
*
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
" ;
The "2" in the " Â
![\frac{2}{1}](/tpl/images/0075/2141/40438.png)
 "Â
   cancels to "1" ; and the "4" in the "
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
"Â
   cancels to "2" ;  {Since:  "(4÷2=2)" ; and since:  "(2÷2=1)" ;
  →  and we have:  " 2*
![\frac{49}{4}](/tpl/images/0075/2141/a1f07.png)
= " Â
![\frac{49}{2}](/tpl/images/0075/2141/43c6f.png)
 " .
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Note: Â {2*10] = 20 .
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So; we can rewrite our equation as follows:
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→ " P = Â
![\frac{49}{2}](/tpl/images/0075/2141/fc3a6.png)
 +  20 −
![\frac{17}{6}](/tpl/images/0075/2141/0b52f.png)
 " ; Â
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Now, multiply the entire equation (both sides) by "6" ;
                    to get rid of the fractions;
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→ 6*{P = Â
![\frac{49}{2}](/tpl/images/0075/2141/fc3a6.png)
 +  20 −
![\frac{17}{6}](/tpl/images/0075/2141/0b52f.png)
} ;
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to get:
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  → 6P = (
![\frac{6}{2}](/tpl/images/0075/2141/a5cbf.png)
*49)  +  20  −  (6*
![\frac{17}{6}](/tpl/images/0075/2141/0b52f.png)
) ;
 → 6P = (3 * 49) + 20  −  (
![\frac{6}{6}](/tpl/images/0075/2141/ab254.png)
* 17) ;
       →  6P = ( 3 * 49) + 20  −  (1 * 17)  ;
       →  6P = ( 3 * 49) + 20  −  (1 * 17)  ;
       →  6P =  (147) + 20 − 17 ;
       →  6P = 147 + 20 − 17 ;
       →  6P  = (147 + 20) − 17 ;
Â
       →  6P = 167 − 17 ;
       →  6P = 150 ;
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Now, divide EACH SIDE of the equation by "6" ; to isolate "P" on one side of the equation; and to solve for "P" (which is our answer, in units of "feet" (ft). ;
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       → 6P / 6  =  150 / 6 ;
to get:  →  P = 25 .
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The answer is: Â "25 feet" .
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