Answer
Length: $12$ feet
Width: $5$ feet
Work Step by Step
Let's note:
$l$=the length of the rectangle
$w$=the width of the rectangle
We can write the system of equations:
$\begin{cases}
2l+2w=34\\
4l-3w=33
\end{cases}$
Use the addition method: multiply Equation 1 by -2 and add it to Equation 2 to eliminate $l$ and determine $w$:
$\begin{cases}
-2(2l+2w)=-2(34)\\
4l-3w=33
\end{cases}$
$\begin{cases}
-4l-4w=-68\\
4l-3w=33
\end{cases}$
$-4l-4w+4l-3w=-68+33$
$-7w=-35$
$w=\dfrac{-35}{-7}$
$w=5$
Substitute the value of $w$ in Equation 1 to find $l$:
$2l+2w=34$
$2l+2(5)=34$
$2l+10=34$
$2l=34-10$
$2l=24$
$l=12$
The system's solution is:
$l=12$
$w=5$
