The rhombus has a perimeter of 200 and the diagonals are 4: 3. Determine the area of the rhombus.

Since the lengths of all sides of a rhombus are equal, we define these lengths through the rhombus perimeter. AB = BC = CD = AD = P / 4 = 200/4 = 50 cm.

The diagonals of the rhombus are related as 4/3, and since the diagonals at the point O are divided in half, the ratio of the halves of the diagonals OA / OB = 4/3.

Let the length OB = 3 * X cm, then OA = 4 * X cm.

In a right-angled triangle AOB, according to the Pythagorean theorem, AB ^ 2 = OB ^ 2 + OA ^ 2.

2500 = 9 * X ^ 2 + 16 + X ^ 2.

25 * X ^ 2 = 2500.

X ^ 2 = 2500/25 = 100.

X = 10 cm.

Then RH = 30 cm, and then BD = 2 * 30 = 60 cm.

ОА = 40 cm, and then АС = 2 * 40 = 80 cm.

Determine the area of ​​the rhombus.

S = АС * ВD / 2 = 60 * 80/2 = 2400 cm2.

Answer: The area of ​​the rhombus is 2400 cm2.