Question 247312
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Let us see the room (being rectangle):
{{{drawing(350,350, -1,5,-1,3,line(0,0,0,2),line(0,2,4,2),line(4,2,4,0),line(4,0,0,0),locate(.2,1,W= green(x)), locate(1.8,2.2,L= green(x+9ft)))}}}


{{{Area[R]=L*W=(x+9)(x)}}}
{{{322ft^2=x^2+9x}}}
{{{x^2+9x-322=0}}}, where{{{system(a=1,b=9,c=-322)}}}
Solving discriminant:
{{{b^2-4ac=9^2-4(1)(-322)=81+1288=1369}}}


Continuing the quadratic eqn:
{{{x=(-9+-sqrt(1369))/(2(1))}}}
{{{x=(-9+-37)/2}}}
2 values:
{{{x=(-9+37)/2=28/2=red(14ft=Width)}}}, use (Answer)
{{{x=(-9-37)/2=-46/2=-23}}}, discard

Length: {{{9+14=red(23ft)}}}
Check,
{{{A=L*W}}}
{{{322ft^2=(23)(14)}}}
{{{322ft^2=322ft^2}}}


Thank you,
Jojo</font>