#### Answer

The dimensions are 4 m by 9 m.

#### Work Step by Step

Let us consider the length as $ L $ and width as $ W $. Therefore, from the given conditions, $\begin{align}
& LW=36\ \text{square meters} \\
& L=2W+1
\end{align}$
Therefore, put the value of $ W $ from equation $ L=2W+1$ in equation, $ LW=36$. So,
$\begin{align}
& LW=36 \\
& \left( 2W+1 \right)W=36 \\
& 2{{W}^{2}}+W-36=0
\end{align}$
Solving further
$\begin{align}
& W(2W+9)-4(2W+9)=0 \\
& (W-4)(2W+9)=0
\end{align}$
And, $ W=4,W=\frac{-9}{2}$
Take the positive value of the width.
Now, find the value of the length.
$\begin{align}
& W=2W+1 \\
& =2\times 4+1 \\
& =9\ \text{m}
\end{align}$
Thus, the dimension of the rectangle is 4 meters by 9 meters.