Question 97846
you were close 
the place where you erred was in taking the length as 30 -x
Since its a path running around you have to consider 2 sides.So the length 
would be 30 -2x and the width 20 -2x
Now you can procced as earlier,

(30-2x)(20-2x)=400
600-100x + 4x^2 =400
4x^2 -100x +200=0
x^2 -25x + 50 =0
x= (25 +- 5sqrt(17))/2
 
we take only 
(25 - 5sqrt(17))/2  since the other root makes the widt greater than the side
=2.192 ft