8. A square is divided into three congruent rectangles. The middle rectangle is removed and replaced on the side of the original square to form an octagon as shown.
What is the ratio of the length of the perimeter of the square to the length of the perimeter of the octagon?
A $3: 5$
B $2: 3$
C $5: 8$
D $1: 2$
E $1: 1$
Solution: A
Suppose that the square has side length $3 x$. Then the square has perimeter of length $4 \times 3 x=12 x$.

Each rectangle has size $3 x \times x$. So we see that the octagon has a perimeter length
$$
4 x+3 x+4 x+x+3 x+x+3 x+x=20 x .
$$

Hence ratio of the lengths is $12 x: 20 x=3: 5$