# Find the area of a rhombus if its diagonals are 3: 4 and the side is 10.

September 24, 2021 | education

| Let the length of the diagonal BD = 3 * X cm, then AC = 4 * X cm.

The diagonals of the rhombus at the point of their intersection are halved and intersect at right angles. Then AO = OS = AC / 2 = 4 * X / 2 = 2 * X cm, OB = OD = BD / 2 = 3 * X / 2 = 1.5 * X cm, and triangle AOB is rectangular.

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

100 = 4 * X ^ 2 + 2.25 * X ^ 2 = 6.25 * X ^ 2.

X ^ 2 = 100 / 6.25 = 16.

X = 4.

Then AC = 4 * 4 = 16 cm, BD = 3 * 4 = 12 cm.

Determine the area of the rhombus.

Savsd = АС * ВD / 2 = 16 * 12/2 = 96 cm2.

Answer: The area of the rhombus is 96 cm2.

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