Question 404844
The area of a rectangle is {{{S=L*W}}}, when L is the length, W is the width, so {{{L*W=36}}}
The perimeter af a rectangle is {{{P=2*(L+W)}}}, so {{{2*(L+W)=36}}}, {{{L+W=18}}}
So, the system of equations
{{{L*W=36}}}
{{{L+W=18}}} From the second equation {{{W=18-L}}}, put it in the first equation
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{{{L*(18-L)=36}}}
{{{18L-L^2=36}}}
{{{L^2-18L+36=0}}}
 {{{L = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
 {{{L = (-(-18) +- sqrt( (-18)^2-4*1*36 ))/(2*1) }}} 
 {{{L = (18 +- sqrt( 180))/2 }}} 
 {{{L1 =9 +15sqrt( 0.2)=15.7}}} or {{{L2=9-15sqrt(0.2)=2.3}}}
{{{W1=18-(9+15sqrt(0.2))=9-15sqrt(0.2)=2.3}}}  or {{{W2=18-(9-15sqrt(0.2))=9+15sqrt(0.2)=15.7}}}
Answer 15.7inches and 2.3inches
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Are you sure that numbers in your problem is correct?The area of a rectangle is 36 square inches. The perimeter of the rectangle is 36 inches.