Three squares with the same centre and corresponding parallel sides are drawn. The distance between the sides of successive squares is 3 and the side length of the largest square is 22 , as shown. What is the perimeter of the smallest square?
(A) 40
(D) 64
(B) 100
(C) 10
(E) 20

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-138.jpg?height=426&width=390&top_left_y=2015&top_left_x=1320)
Three squares with the same centre and corresponding parallel sides are drawn. The distance between the sides of successive squares is 3 and the side length of the largest square is 22 , as shown. What is the perimeter of the smallest square?
(A) 40
(B) 100
(C) 10
(D) 64
(E) 20

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-230.jpg?height=494&width=447&top_left_y=241&top_left_x=1403)

## Solution

Each side of a square will decrease by 6 units each time it gets smaller. The second square will thus have a side length of $22-6=16$ and the smallest square will then have a side length of 10 .

Its perimeter is $4 \times 10$ or 40 .

ANSWER: (A)