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?

Question

Mathematics

Ramsey

23 May, 17:10

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?

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Davidson · Answer 1

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.