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The area of a rectangle is 80 sq ft. If the width is increased by 1 foot and the length is decreased by 1 foot, the new rectangle has area 90 sq ft. What is the perimeter of the original rectangle, in feet?

 Jun 1, 2020
 #1
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\(S_1*S_2 = 80\)

 

\([S_1+1]*[S_2-1] = 90\)

\(S_1 = {80\over S_2}\)

\([{80\over S_2}+1]*[S_2-1]=90\)

\([{80+S_2\over S_2}]*[{S_2-1\over 1}]=90\)

\({{80S_2-80+(S_2)^2-S_2}\over S_2}=90\)

\({{80S_2-80+(S_2)^2-S_2}} =90S_2\)

\({{80S_2-80+(S_2)^2-S_2-90S_2}} =0\)

\({-80+(S_2)^2-11S_2} =0\)

\((S_2)^2 -11S_2-80 =0\)

\(S_2=16\)

\(S_1 = 5\)

 

 

\(p = 42\)

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 Jun 1, 2020

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