Let [tex]L[/tex] be the length of the rectangle and [tex]W[/tex] be the width. In the problem it is given that [tex]L=2W-3[/tex]. It is also given that the area [tex]LW=27[/tex]. Substituting in the length in terms of width, we have [tex]W(2W-3)=27 \\ 2W^2-3W-27=0 \\ (2W-9)(W+3)=0[/tex]. Using the zero product property, [tex]2W-9=0 \text{ or } W+3=0[/tex]. Solving these we get the width [tex]W=4.5 \text{ or } -3[/tex]. However, it doesn't make sense for the width to be negative, so the width must be [tex]\boxed{4.5 \text{ m}}[/tex]. From that we can tell the length [tex]L=2(4.5)-3=\boxed{6 \text{ m}}[/tex].
