Answer
$20 m^2$
Work Step by Step
As per question, we have $(20+2x)(10+2x)=600$
or,$200+40x+20x+4x^2-600=0$
or, $x^2+15x+50-150=0$
or, $x^2+15x-100=0$
Thus, $(x-5)(x+20)=0$
This implies $x=-20,5$
Since, the length cannot be negative, thus $x=5$ and Path width$=10+2x=10+2(5)=20 m^2$
