Question 126270
Let us begin by assigning variables to the length and height of the rectangle, it is also called base and height, so as long as you are assigning the correct variable to the correct side you should be ok.  Remember if taking a test, use the notation {{{P=2b+2h}}}
             Perimeter equals 2 times the base plus 2 times the height.

1. Let the width be W and the Lenght be L.

2.  The formula for a perimiter of a rectangle is P=2l+2w (2 times the lenght plus 2 times the width)

3. In this problem the length is 2 inches greater than 2 times the width so let us set L to {{{(2*w)+2}}} and W will remain the same.

4.  Now let us plug these values into our formula.
       {{{34=2*((2*w)+2)+2*w}}}

5.  Now all that is left is to solve for W.  We solve this just like any single variable equation.  We need to isolate the W to one side of the equation.

Remember the order of operations when doing problems.
                   {{{34=2*((2*w)+2)+2*w}}}  
First let us use the distributive property of multiplication.  We need to multiply {{{(2*w)+2}}} by 2.  
This gives us {{{4w+4)}}}

So now our formula looks like this {{{34=4w+4+2w}}} or to simplfy {{{34=6w+4}}}

Now we need to subtract 4 from each side of the equation
{{{34-4=6w+4-4}}}
Which gives us {{{30=6w}}}

Now divide each side of the equation by 6
{{{30/6=6w/6}}}

This leaves us with {{{5=w}}}

Now we have determined that the W or width of our rectangle is 5.  The next step is to check our work by plugging in 5 for the w in our perimeter equation.

{{{34=2*(2w+2)+2w}}}
{{{34=(2*(2*5)+2)+2*5}}}  replacing w with 5
{{{34=(2*(10)+4)+10}}}    following order of operations, multiplication
{{{34=20+4+10}}}          addition
{{{34=34}}}               result

So our width is 5, now to figure our length  with is {{{(2*5)+2}}} or {{{10+2}}} which simplifies to 12.

Answers   Width 5   Length 12

Simple check   {{{34=2*5+2*12}}}
               {{{34=10+24}}}
               {{{34=34}}}