Answer
$5\ m$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ represents the width of the path around the pool.
Step 2. The dimensions of the larger rectangle are $10+2x$ by $20+2x$, and the area is given by $(10+2x)(20+2x)=600$
Step 3. Simplify the above equation to get $(5+x)(10+x)=150$, $x^2+15x+50=150$ and $x^2+15x-100=0$
Step 4. Solving the above equation by factoring, we have $(x+20)(x-5)=0$; discard the negative solution to get $x=5\ m$
