The perimeter p of the path is the sum of eight segments. We'll start at the bottom right and go around clockwise.
p = (20 + x) + (10 + 2x) + (20 + x) + x + 20 + 10 + 20 + x
112 = 6x + 100
12 = 6x
x = 2
Answer: 2 meters
Area of the path; three patches:
A = x(20 + x) + 10 x + x(20 + x) = 50x + 2x^2
A = 50(2) + 2(2)^2 = 108
Answer: 108 sq meter
