Question 37922
Start with the formula for the perimeter of a rectangle:
{{{P = 2L+2W}}}
In your problem, P = 40ft.
{{{W = L/2 + 2}}}
{{{L = L}}} 
Substitute these into the basic formula above:
{{{40 = 2L + 2(L/2 + 2)}}} Simplify and solve for L
{{{40 = 2L + L + 4}}}
{{{40 = 3L + 4}}} Subtract 4 from both sides of the equation.
{{{36 = 3L}}} Divide both sides by 3.
{{{12 = L}}}
The length is 12ft.
The width is{{{L/2+2 = 12/2 + 2}}} = 8ft.
Check: 
{{{P = 2L+2W}}}
{{{P = 2(12)+2(8)}}}
{{{P = 24+16}}}
{{{P = 40}}} It checks!