Question 455939

the area of the rectangle is {{{A=L*W}}}


The length {{{L}}} is 3m less than twice its width {{{W}}}: {{{L+3m=2W}}}...->...{{{L=2W-3m}}}

{{{A=L*W}}}

{{{27m^2=(2W-3m)*W}}}

{{{27m^2=2W^2-3m*W}}}

{{{2W^2-3Wm-27m^2=0}}}....use quadratic formula

{{{W = (-(-3m) +- sqrt( (-3m)^2-4*2*(-27m^2) ))/(2*2) }}}

{{{W = (3m +- sqrt( 9m^2+216m^2) ))/4 }}}

{{{W = (3m +- sqrt( 225m^2) ))/4 }}}

{{{W = (3m +- 15m ))/4 }}}...you need only positive root because width cannot be negative


{{{W = (3m + 15m )/4 }}}

{{{W = (18m )/4 }}}

{{{W = 4.5m  }}}......now find the {{{L}}}


{{{L=2*4.5m -3m}}}

{{{L=9m -3m}}}

{{{L=6m}}}