Question 101805
L – Length
W – Width
From your explanation, 
L = 2 + 3W
The perimeter,P, of a rectangle is the sum of twice the width and twice the length or P=2L+2W.

P = 2L + 2W
P = 2(2+3W) + 2W Substitute from above for L. 
P = 2(2)+ 2(3W)+ 2W Distributive Property. 
P=4+6W+2W Simplify. 
P=4+8W

From your explanation, the perimeter must be less than 28 feet or P<28 ft.

P<28
4+8W<28 Substitute.
4-4+8W<28-4 Additive inverse of 4 or (-4).
8W<24 
8W/8<24/8 Multiplicative inverse of 8 or (1/8)
W<3
Since W is less than 3 and must be an integer, then the maximum value it can have is 2. 
W=2 ft.