Question 547501
<pre>
P = 2L + 2W = 24        <--- perimeter formula

      L + W = 12        <--- divided through by 2

          W = 12 - L    <--- solved for W

          W &#8807; 1        <--- 1 is least possible value for width 

     12 - L &#8807; 1        <--- Substituted 12 - L for W

         -L &#8807; -11      <--- Subtracted 12 from both sides
     
          L &#8806; 11       <--- Divided both sides by -1, reversed inequality

      L + W = 12       <--- from 2nd step above

          L = 12 - W   <--- Solved for L  

          L &#8807; 1        <--- 1 is least possible value for length

     12 - W &#8807; 1        <--- Substituted 12 - W for L

         -W &#8807; -11      <--- Subtracted 12 from both sides

          W &#8806; 11       <--- Divided both sides by -1, reversed inequality
  
      1 &#8806; L &#8806; 11      <--- From above

      1 &#8806; W &#8806; 11      <--- From above 

L  1  2  3  4  5  6  7  8  9 10 11
----------------------------------
W 11 10  9  8  7  6  5  4  3  2  1

It looks like there are 11, but there are only 

6 possibilities, because for instance,

a 5ft x 7ft and a 7ft x 5ft are the same size.

The 6 possibilities are:

1.   1ft×11ft
2.   2ft×10ft
3.   3ft×9ft
4.   4ft×8ft
5.   5ft×7ft
6.   6ft×6ft

Edwin</pre>