Question 1131622
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One equation is 

   L = 2W + 1,       (1)

as the tutor @LoverMath1 derived in her post.


The other equation is

    {{{sqrt(W^2 + L^2)}}} = 2W + 4.

which follows from the condition.


This second condition, due to (1), is the same as

    {{{sqrt(W^2 + (2W+1)^2)}}} = 2W + 4.     (2)


Equation (2) is your basic equation to solve.   Square both sides

    W^2 + 4W^2 + 4W + 1 = 4W^2 + 16W + 16

    W^2 - 12W - 15 = 0.


<U>Answer</U>.  The dimensions of the rectangle are  W = {{{(12+sqrt(204))/24}}}  and  L = 2W+1 = {{{(48+2sqrt(204))/24}}} feet.
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