The diagonals of the rhombus are 2 and 2√3. Find the height of the rhombus.

univerkov | June 23, 2021 | education

Knowing the lengths of the diagonals of the rhombus, we determine its area.

Savsd = AC * BD / 2 = 2 * √3 * 2/2 = 2 * √3 cm2.

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

Then triangle AOB is rectangular, AO = AC / 2 = 2 * √3 / 2 = √3 cm, OB = BD / 2 = 2/2 = 1 cm.

By the Pythagorean theorem, AB ^ 2 = OA ^ 2 + OB ^ 2 = 3 + 1 = 4.

AB = 2 cm.

Savsd = 2 * √3 = AB * KН.

KН = 2 * √3 / AB = 2 * √3 / 2 = √3 cm.

Answer: The height of the rhombus is √3 cm.

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