The rectangle in the figure is divided into eight squares. The side of the smallest square measures $1 \mathrm{~cm}$.

(a) What are the lengths of the sides of the other squares?

(b) What is the perimeter of this rectangle?

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-024.jpg?height=280&width=214&top_left_y=1456&top_left_x=1589)
(a) Since the smallest square has a side of $1 \mathrm{~cm}$, the side of square $A$ measures $1 \times 4=4 \mathrm{~cm}$ and the side of square $B$ measures $4+1=5$ $\mathrm{cm}$. Square $C$ shares a side with square $B$, so square $C$ also has a side of $5 \mathrm{~cm}$. Therefore, the side of the largest square measures $5+5+4=14 \mathrm{~cm}$.

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-075.jpg?height=328&width=240&top_left_y=287&top_left_x=1548)

(b) The sides of the rectangle measure $14 \mathrm{~cm}$ and $14+5=19 \mathrm{~cm}$, so the perimeter of the rectangle is $14 \times 2+19 \times 2=66 \mathrm{~cm}$.