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.
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