The sum of the two sides of a rectangle is 8 cm, and the sum of its three sides is 10 cm. What can be the perimeter of the rectangle?

Suppose we are given the sum of two perpendicular (not opposite each other) sides. Then you get a square, because all sides will be equal. Then the sum of the three sides will be equal to 12. And our sum of the three sides is equal to 10. It turns out that the sum of the two sides lying opposite each other is given.
It turns out that each of the two opposite sides is 4 cm.
Suppose we are given the sum of two opposite sides, the length of which we know, and one non-opposite side. Then it turns out that the other side will be equal:
10 – 4 – 4 = 2 (cm)
And the perimeter of the rectangle will be:
(2 + 4) * 2 = 6 * 2 = 12 (cm)
But if we assume that we are given the sum of two opposite sides, the sum of which is unknown to us, and one non-opposite side, the length of which we know – 4 cm, then the other side will be equal:
(10-4) / 2 = 3 (cm)
And the perimeter will be:
(3 + 4) * 2 = 14 (cm)
It turns out that the perimeter of the rectangle is either 12 cm or 14 cm.
Answer: 12 cm or 14 cm.