The answer is: "25 feet"
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Explanation:
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Perimeter = 2*(length) + 2*(width);
or; "P = 2L + 2w " ;.
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In this case:
"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 ;
w = 10 ;
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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 = [tex] \frac{48+1}{4} [/tex] = [tex] \frac{49}{4}[/tex] " ;
→ " 2 ⅚ = [ (6*2) + 5 ] / 6 = [tex] \frac{12+5}{6} [/tex] = [tex] \frac{17}{6}[/tex] " ;
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Rewrite our equation:
→ " P = { [2* (12 ¼) ] + [2* 10] } − 2 ⅚ " ;;
substituting the "mixed numbers" with "improper fractions" ;
→ " P = { [2* ([tex] \frac{49}{4}[/tex]) + [2* 10] } − [tex] \frac{17}{6}[/tex] " ;
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→ Note: " 2*[tex] \frac{49}{4}[/tex] ;
= [tex] \frac{2}{1} [/tex] *[tex] \frac{49}{4}[/tex] " ;
The "2" in the " [tex] \frac{2}{1} [/tex] "
cancels to "1" ; and the "4" in the " [tex] \frac{49}{4}[/tex] "
cancels to "2" ; {Since: "(4÷2=2)" ; and since: "(2÷2=1)" ;
→ and we have: " 2*[tex] \frac{49}{4}[/tex] = " [tex] \frac{49}{2} [/tex] " .
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Note: {2*10] = 20 .
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So; we can rewrite our equation as follows:
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→ " P = [tex] \frac{49}{2}[/tex] + 20 − [tex] \frac{17}{6}[/tex] " ;
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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 = [tex] \frac{49}{2}[/tex] + 20 − [tex] \frac{17}{6}[/tex] } ;
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to get:
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→ 6P = ([tex] \frac{6}{2}[/tex] *49) + 20 − (6*[tex] \frac{17}{6}[/tex]) ;
→ 6P = (3 * 49) + 20 − ([tex] \frac{6}{6} [/tex] * 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 ;
→ 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: "25 feet" .
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