Question 164449
To help you set it up:
Imagine the 18 x 13 rectangle is already on the ground. Now imagine a border around that rectangle. What you have is a 'rectangle inside a rectangle'. The area you care about is the difference in the areas of the two rectangles. Assume the path is the same width all the way around. Let that width = X
Area of rectangle is {{{A = Length*Width}}}

The inside rectangle is given as 18 x 13 = {{{234}}}
The area of the outer rectangle is given as
{{{Width = 13 + 2W}}}
{{{Length = 18 + 2W}}}
{{{AreaOfBorder = AreaOfOuterRecntangle - AreaOfInnerRectangle }}}
{{{516 = (13+2W)(18+2W) - 234 }}}
{{{516 = 234 + 62W + 4W^2 - 234}}}
Now collect like terms, move everything to one side and solve

If you need more help, let me know