Let l and w be the length and width of the rectangle, respectively; therefore, according to the question
[tex]\begin{gathered} l=2w+1 \\ and \\ l*w=45 \end{gathered}[/tex]Where l and w are in meters.
Substitute the first equation into the second one, as shown below
[tex]\begin{gathered} l=2w+1 \\ \Rightarrow(2w+1)*w=45 \\ \Rightarrow2w^2+w=45 \\ \Rightarrow2w^2+w-45=0 \end{gathered}[/tex]Solve for w using the quadratic formula,
[tex]\begin{gathered} \Rightarrow w=\frac{-1\pm\sqrt{1+4*2*45}}{2*2}=\frac{-1\pm\sqrt{361}}{4}=\frac{-1\pm19}{4} \\ \Rightarrow w=\frac{9}{2},-5 \end{gathered}[/tex]But w has to be positive since it is a measurement; therefore, w=9/2.
Finding l given the value of w=9/2,
[tex]\begin{gathered} w=\frac{9}{2} \\ \Rightarrow l=2(\frac{9}{2})+1=10 \\ \Rightarrow l=10 \end{gathered}[/tex]Thus, the answers are length=10 m, width=4.5m
