Calculate the distance between the sides of the rhombus if its diagonals are 12 cm and 16 cm, and the side is 1 dm.

The distance between the sides of the rhombus is the HP perpendicular between the opposite sides.
Let us prove that the AOD triangle is similar to the DOН triangle.
Let the DAO angle = α, then the AOН angle = 180 – 90 – α = 90 – α.
Angle DOН = 90 – AOН = 90 – (90 – α) = α. Consequently, the angle DAO = DOН, and the AOD triangle is similar to the DOН triangle in an acute angle.
Then:
AD / OD = AO / OH.
AO = AC / 2 = 16/2 = 8 cm.
OD = ВD / 2 = 12/2 = 6 cm.
10/6 = 8 / OH.
OH = 6 * 8/10 = 4.8 cm.
Then HP = 2 * OH = 2 * 4.8 = 9.6 cm.
Answer: The distance between the sides of the rhombus is 9.6 cm.