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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