Answer :

AL2006

If you don't mind being around fractions and decimals, then there are an
infinite number of possible rectangles with the perimeter of 14.

If you'd rather just stick with whole numbers, then there are three choices:
 
--  1 unit by 6 units

--  2 units by 5 units

--  3 units by 4 units
Let W be the width and L be the length:

2W + 2L = 14

W + L = 7

(W,L) = (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)