Calculate the perimeter of a rhombus if the lengths of its diagonals are 12 cm and 16 cm.

The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.

Then AO = CO = AC / 2 = 16/2 = 8 cm, BO = DO = BD / 2 = 12/2 = 6 cm.

The triangle AOB is rectangular, then, by the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AO ^ 2 + BO ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Since the lengths of all sides of a rhombus are equal, the perimeter of the rhombus is: Ravsd = 4 * AB = 4 * 10 = 40 cm.

Answer: The perimeter of the rhombus is 40 cm.