Question 701552
Removed earlier solution because was wrong, rechecked twice more, different but still wrong. 

Two rectangles.  Inner and outer.  Inner is just factory area.  Outer is the area of lawn and factory combined.  Let x be distance from inner side to corresponding outer side, away from the corners locations.  Know that the lawn includes four squares of x^2 area.  Draw this picture.


Outer area rectangle = (120+2x)(80+2x)
The outer area is TWO times the inner area,
Outer area (120+2x)(80+2x)=2(120)(80)
2*2*(60+x)(40+x)=2*2*60*80
(60+x)(40+x)=4800
.
.
{{{x^2+100*x-2400=0}}}

Use general solution to quadratic equation,
{{{x=(-100+- sqrt(100^2-4*(-2400)))/2}}}
{{{x=(-100+- 140)/2}}}
x= 20  the width. (the  -140  number in expression is not sensible)