The diagonals of the rhombus are 80 cm and 60 cm. Find the distance between the parallel sides of the rhombus.

By the condition of the problem, the diagonals of the rhombus are known, we can find the area of the rhombus:
S = d1 * d2 / 2 = 80 * 60/2 = 2400 (cm²).
By the Pythagorean theorem, we find the side of the rhombus:
a = √ ((d1 / 2) ² + (d2 / 2) ²) = √ (40² + 30²) = √2500 = 50 (cm).
The distance between the parallel sides of the diamond is the height of the diamond.
We write down the formula for the area of a rhombus through the side and the height and from it we find the height:
S = a * h → h = S / a = 2400/50 = 48 (cm).
Answer: the distance between the parallel sides is 48 cm.