The side of the rhombus is 5 cm, and one of its diagonals is 6 cm. Find the distance from the center of the rhombus to its side.

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

Then ОВ = ВD / 2 = 6/2 = 3 cm, and triangle AOB is rectangular.

In a right-angled triangle AOB, according to the Pythagorean theorem, we determine the length of the leg AO.

AO ^ 2 = AB ^ 2 – OB ^ 2 = 25 – 9 = 16.

AO = 4 cm.

Determine the area of the triangle AOB.

Saov = AO * VO / 2 = 4 * 3/2 = 6 cm2.

Also Saov = AB * OH / 2.

OH = 2 * Saov / AB = 2 * 6/5 = 12/5 = 2.4 cm.

Answer: From the center of the rhombus to its side 2.4 cm.