P = 2L + 2W = 24 <--- perimeter formula
L + W = 12 <--- divided through by 2
W = 12 - L <--- solved for W
W ≧ 1 <--- 1 is least possible value for width
12 - L ≧ 1 <--- Substituted 12 - L for W
-L ≧ -11 <--- Subtracted 12 from both sides
L ≦ 11 <--- Divided both sides by -1, reversed inequality
L + W = 12 <--- from 2nd step above
L = 12 - W <--- Solved for L
L ≧ 1 <--- 1 is least possible value for length
12 - W ≧ 1 <--- Substituted 12 - W for L
-W ≧ -11 <--- Subtracted 12 from both sides
W ≦ 11 <--- Divided both sides by -1, reversed inequality
1 ≦ L ≦ 11 <--- From above
1 ≦ W ≦ 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