Question 461273
Area: {{{A=34m^2}}}

length is {{{L=(x-4)m}}}
Width is {{{W=(x+11)m}}}

{{{A=LW}}}

{{{34m^2=(x-4)m*(x+11)m}}}

{{{34m^2=(xm-4m)*(xm+11m)}}}

{{{34m^2=(xm)^2+11xm*m-4xm*m-44m^2}}}


{{{34m^2=(xm)^2+7xm^2-44m^2}}}

{{{0=(xm)^2+7xm^2-44m^2-34m^2}}}

{{(x^2m^2+7xm^2-78m^2=0}}}

{{{((x)^2+7x-78)m^2=0}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-7 +- sqrt( 7^2-4*1*(-78) ))/(2*1) }}}


{{{x = (-7 +- sqrt( 49+312 ))/2 }}}



{{{x = (-7 +- sqrt(361 ))/2 }}}


{{{x = (-7 +- 19)/2 }}}.we will take only positive root; length and width cannot be negative

{{{x = (-7 + 19)/2 }}}


{{{x = 12/2 }}}

{{{x = 6}}}....now find {{{L=(x-4)m}}} and {{{W=(x+11)m}}}

{{{L=(6-4)*m=2m}}}

{{{W=(6+11)*m=17m}}}