Explanation:
Area of the rectangle = 9×6 = 54 m²
Area of the path is also 54 m²
so total area of the bigger rectangle is 54+54 = 108 m²
now the ratio of length to width is 9:6 or, 3:2
so, for 108 m²
(3x)(2x) = 108
6x²=108
x²=18
x=3√2
So length = 3x = 9√2 and width = 2x = 6√2