The perimeter of a rectangle, one side of which is 40% of the other, is 21 cm. Find the sides of the rectangle.

1. Find the part of the side that is equal to 40% of the other side:
40/100 = 4/10 = 2/5.
2. Let one side of the rectangle be equal to p, then the other is equal to p * 2/5.
3. Draw up the equation for the perimeter of a rectangle according to the formula P = 2 * (a + b), where P is the perimeter of a rectangle with length and width a and b:
21 = 2 * (p + p * 2/5),
21/2 = 7p / 5,
21/2 * 5/7 = p,
15/2 = p,
p = 7.5.
4. Find the second side of the rectangle:
2/5 * 7.5 = 3.
Answer: one side is 7.5 cm and the other is 3 cm.