Answer
The dimensions are
Length $=8 \; feet$
Width $=3 \; feet$
Work Step by Step
Let the length is $l$. and the width is $w$.
length is 2 feet more than twice its width.
In the equation form
$l=2w+2$ ... (1)
The perimeter of the garden is
$P=2(l+w)$ ... (2)
In the question we have perimeter equal to length of fencing.
$P=22 \; feet$
Plug into equation 2
$22=2(l+w)$ Plug the value of $l$ from equation (1).
$22=2(2w+2+w)$
Divide both sides by $2$.
$11=3w+2$
Isolate $w$.
$w=\frac{11-2}{3}$
$w=\frac{9}{3}$
$w=3$ plug into equation (1).
$l=2(3)+2$
$l=6+2$
$l=8$.
