Given a rhombus with diagonals equal to 2 dm and 4.8 dm. Find the side of this diamond.

univerkov | May 19, 2021 | education

The diagonals of the rhombus, at the point of their intersection, are halved and intersect at right angles.

Then AO = CO = AC / 2 = 2/2 = 1 dm, BO = DO = BD / 2 = 4.8 / 2 = 2.4 dm.

The ABO triangle is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse AB. AB ^ 2 = AO ^ 2 + BO ^ 2 = 1 + 5.76 = 6.76.

AB = 2.6 dm.

In a rhombus, the lengths of all sides are equal, then AB = BC = CD = AD = 2.6 dm.

Answer: The length of the sides of the rhombus is 2.6 dm.

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