Arectangle has width 12 inches and length 3 inches. every dimension of the rectangle is multiplied by 1/3 to form a similar rectangle. how is the ratio of the perimeters related to the ratio of the corresponding sides?

Ratio of perimeter with the sides will be the same

The first rectangle has 12 inches width and 3 inches length. Then the perimeter of this rectangle is :
Perimeter 1: 2x( 12+3) inches= 30 inches.
Perimeter 1 to width ratio = 30/12 = 2.5
Perimeter 1 to length ratio: 30/3= 10

The second rectangle has 1/3 dimension, thus its width is 4 inches and its length is 1 inches. Then the perimeter is:
Perimeter 2: 2x( 4+1) inches= 10 inches
Perimeter 2 to width ratio = 10/4 = 2.5
Perimeter 2 to length ratio: 10/1= 10

The perimeter ratio is same since it will shorten the same ratio as the length and width.