A rectangle 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?

Respuesta :

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.