Question 848560
One MUST assign variables.
w=width
L=Length
{{{wL=44}}}------direct translation from description
{{{2L=-5+2w}}}------direct translation from description
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Capital L was chosen for easier reading in order to not confuse digit one with lower-case L.
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Using area, w=44/L.
Substituting into dimensions equation, {{{2L=-5+2(44/L)}}};
{{{2L=88/L-5}}}
{{{2L*L=(88/L)L-5L}}}
{{{2L^2=88-5L}}}
{{{highlight_green(2L^2+5L-88=0)}}}.
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Guessing that the quadratic is not factorable, use general solution.
Discriminant, 5*5-4*2(-88)=25+8*8*11=25+11*64=25+704=729
{{{L=(-5+sqrt(729))/(2*2)}}}, we must use the positive square root form.
{{{L=(-5+27)/4}}}
{{{highlight(L=11/2)}}}, which is same as 5.5 feet or 5 feet 6 inches.
{{{w=44/L=44/(11/2)=44*2/11=highlight(8)}}}, 8 feet.


Knowing L and w, you can now find the perimeter.
{{{highlight_green(highlight(2w+2L=perimeter))}}}