you have rectangle 100x130

the sidewalk plus the parking lot equals: (100+2s)x(130+2s)

the area is therefore: (100+2s)x(130+2s)=13000+260s+200s+4s^2=4s^2+460s+1 3000

now subtract the original rectangle area (100x130=13000) from the sidewalk+parking lot area to get: 4s^2+460s

that expression gives the area of the sidewalk for width "s"

now solve for: 4s^2+460s=1659

which comes out to: s=3.5

so you got it right