The perimeter of the rhombus is 100 cm, and the diagonals are 3: 4. Find the area of the rhombus.

Since the lengths of the sides of the rhombus are equal, then AB = BC = CD = AD = Ravsd / 4 = 100/4 = 25 cm.

Let the length of the smaller diagonal be 3 * X cm, then the length of the larger diagonal is 4 * X cm. The diagonals of the rhombus, at the point of intersection, are halved and intersect at right angles. Then OB = 3 * X / 2 = 1.5 * X, AO = 4 * X / 2 = 2 * X.

By the Pythagorean theorem, AB ^ 2 = AO ^ 2 + OB ^ 2.

625 = 4 * X ^ 2 + 2.25 * X2.

6.25 * X ^ 2 = 625.

X = 10, then BD = 30 cm, AC = 40 cm.

Determine the area of the rhombus.

Savsd = АС * ВD / 2 = 40 * 30/2 = 600 cm2.

Answer: The area of the rhombus is 600 cm2.