Perimeter is the sum of the two lengths plus the sum of the two widths.
Divide the perimeter in half and that is the sum of one length and one width.
27/2 = 13.5
The ratio is 2:1, add the ratio: 2 +1 = 3
Divide the sum by 3:
13.5/3 = 1.5
Multiply that the each portion of the ratio:
4.5 x 2 = 9
4.5 x 1 = 4.5
The length is 9 inches
The width is 4.5 inches