Eight squares with the same centre have parallel sides and are one unit apart. The two largest squares are shown. If the largest square has a perimeter of 96 , what is the perimeter of the smallest square?
(A) 40
(D) 64
(B) 68
(E) 89
(C) 32

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-139.jpg?height=266&width=255&top_left_y=1862&top_left_x=1377)
Eight squares with the same centre have parallel sides and are one unit apart. The two largest squares are shown. If the largest square has a perimeter of 96 , what is the perimeter of the smallest square?
(A) 40
(B) 68
(C) 32
(D) 64
(E) 89

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-258.jpg?height=312&width=309&top_left_y=565&top_left_x=1472)

## Solution

Since the largest square has perimeter 96 , it has a side length of $\frac{96}{4}$ or 24 . From the diagram, the side length of the next square is $24-2$ or 22 . Continuing thus, the side lengths of the eight squares form the sequence: $24,22,20,18,16,14,12,10$. The side length of the eighth square will be 10 giving a perimeter of $4 \times 10=40$.

ANSWER: (A)