SOLUTION: I am absolutely no good at word problems and need all of the help I can get. I appreciate those of you who are helping others, like myself. So thank you very much! The perimet

I am absolutely no good at word problems 

(Remember, though, that word problems are
the ONLY thing algebra is good for!)

and need all of the help I can get.  I appreciate 
those of you who are helping others, like myself.  
So thank you very much!

The perimeter of a rectangle is 44 inches and its 
area is 112 square inches.  Find the the length and 
width of the rectangle.

I know that 2L+2W=44 and that L*W=112  The rest is a 
complete blank as to how to achieve L and W.

Here are the steps, first listed and then done:

1. Solve one of the equations for a letter.
2. Substitute the expression which that letter equals 
   in the OTHER equation.
3. Solve that equation for the value(s) of the letter 
   that it contains.
4. Substitute that value (those values) into one of the 
   original equations.
5. Solve that for the other letter.
6. Now you have the values of both letters, 
   so you are done.

-----------------------------

1.  There are four ways I could begin:
    (a) Pick equation 2L+2W=44 and solve for L.
    (b) Pick equation 2L+2W=44 and solve for W.
    (c) Pick equation LW=112 and solve for L.
    (d) Pick equation LW=112 and solve for W.

    I will arbitrarily pick (a), but I could have 
    picked any of the other three.
 
    2L + 2W = 44
        -2W =      -2W
   ---------------------
    2L      = 44 - 2W

       2L/2 = 44/2 - 2W/2
          L = 22 - W

2.           LW = 112
      (22 - W)W = 112 

3.       22W - W² = 112
   
    Get 0 on the right by subtracting
    112 from both sides:

 22W - W² - 112 = 0 

Rearrange in descending powers of W

 -W² + 22W - 112 = 0

Make the leading term positive by multiplying
every term by -1, which changes all their signs:

 W² - 22W + 112 = 0

Factor or use quadratic if it either won't factor
or because the numbers are too big for you to think
of how to factor it.

 (W - 8)(W - 14) = 0

  Set each factor = 0 and solve it:

  W - 8 = 0 gives solution W = 8
  W - 14 = 0 gives solution W = 14
   
4.  I'll pick 2L+2W=44 to substitute those 
    values into:

     Substituting W = 8

5.  2L + 2(9) = 44
      2L + 18 = 44
          -18  -18
     --------------
      2L      = 26
            L = 26/2
            L = 13

 So one answer is Length = 13, Width = 9  
    
  Substituting W = 14

  2L + 2(14) = 44
    2L + 28 = 44
        -28  -28
   --------------
    2L      = 16
          L = 16/2
          L = 8

 The other answer is Length = 8, Width = 14

6.  You are done except the author of that problem 
    may very well have meant that the length is 
    NEVER shorter than the width.  This is commonly
    done. So if that is the case here, we will
    have to discard the second answer.

Edwin