What is the smallest perimeter of a square if it can be divided without a remainder into a rectangle with sides 18cm and 8cm?

1. Let’s calculate the perimeter of the rectangle, which is equal to:
P = 2 * (a + b) = 2 * (18 + 8) = 2 * 26 = 52 cm.
2. Accordingly, the smallest perimeter of the square, which is divided by the perimeter of the rectangle, will be 52 cm.
Answer: 52 cm.
To check if such a square exists, let’s calculate its side.
The side of the square is:
a = P: 4 = 52: 4 = 13 cm.
Thus, this square is quite correct.