Answer
Length $=8$ feet.
Width $=3$ feet.
Work Step by Step
Step 1:- Let $x$ represent one of the unknown quantitates.
Let the width of a rectangle $=x$.
Step 2:- Represent other unknown quantities in terms of $x$.
The length is $2$ feet greater than twice its width.
Length $=2x+2$
Step 3:- Write an equation in $x$ that models the conditions.
Perimeter equal to twice the length plus twice the width.
From question we have perimeter $=22$ feet.
In the equation form
$\Rightarrow 2(2x+2)+2x=22 $
Step 4:- Solve the equation.
$\Rightarrow 2(2x+2)+2x=22 $
Apply distributive property.
$\Rightarrow 4x+4+2x=22 $
Subtract $4$ from both sides.
$\Rightarrow 4x+4+2x-4=22-4 $
Add like terms.
$\Rightarrow 6x=18 $
Divide both sides by $6$.
$\Rightarrow \frac{6x}{6}=\frac{18}{6} $
Simplify.
$\Rightarrow x=3 $
Thus, width $=3$ feet.
Length $=2x+2=2(3)+2=6+2=8$ feet.
Step 5:- Check the solution.
Perimeter $=22$.
$\Rightarrow 2(8)+2(3)=22$
Simplify.
$\Rightarrow 16+6=22$
Add like terms.
$\Rightarrow 22=22$ True.
