Question 42172
Well let the path have a width x.
Then the garden with the path will have a length 30 + 2x and a width 20 + 2x.
Since the new area is 400, we have
A = LW
400 = (30 + 2x)(20 + 2x)
400 = 600 + 60x + 40x + 4x^2
now rearrange and get
4x^2 + 100x + 200 = 0
x^2 + 25x + 50 = 0 
this does not factor so we use the quadratic
x = (-25 ± sqrt(625-200)) / 2
x = (-25 ± sqrt(425)) / 2
there does not seem to be a solution that works...perhaps you need to rephrase the problem correctly...