Explanation:
Let the length be
[tex]=x[/tex]
Let the width be
[tex]=y[/tex]
The length of a rectangle is 2 meters more than 3 times the width.
This can be represented below as
[tex]x=3y+2[/tex]
The area of a rectangle is calculated with the formula below
[tex]A=l\times w[/tex]
By substituting the values, we will have
[tex]\begin{gathered} A=l\times w \\ A=y(3y+2) \\ 33=3y^2+2y \\ 3y^2+2y-33=0 \end{gathered}[/tex]
By factorizing the quadratic equation, we will have that
[tex]\begin{gathered} 3y^{2}+2y-33=0 \\ 3y^2+11y-9y-33=0 \\ y(3y+11)-3(3y+11)=0 \\ y-3=0,3y+11=0 \\ y=3,3y=-11 \\ y=3,y=\frac{-11}{3} \end{gathered}[/tex]
Hence,
The length will be
[tex]\begin{gathered} x=3y+2 \\ x=3(3)+2 \\ x=9+2 \\ x=11 \end{gathered}[/tex]
Hence,
The final answers are
[tex]\begin{gathered} width=3meters \\ length=11meters \end{gathered}[/tex]
