Let the length be 8x and width be 3x
p=2(l+w)=2(8x+3x)=2(11x)=22x
ratio of width to perimeter=3x:22x=3:22
This ratio does not depend on actual width.
For example
l=16cm w=6cm p=2(16+6)=44cm
l=24cm w=9cm p=2(24+9)=66cm
The ratio of length to width is 8:3 and ratio of width to perimeter is 3:22 in both the cases.