The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. what is the distance between the point of intersection of the diagonals and the side of the rhombus?

Recall that a rhombus is a particular kind of parallelogram: the length you are looking for will be half of the parallelogram's height.

First, find the second diagonal of the rhombus:
d₂ = 2·A / d₁
    = 2·480 / 48       *we transformed the units of measurement from dm to cm
    = 20 cm

Now, consider the small triangle rectangle formed by the side of the rhombus and the halves diagonals. You can apply the Pythagorean theorem in order to find the side:
s = √[(d₁ /2)² + (d₂ / 2)²]
   =√[(48 / 2)² + (20 / 2)²]
   = 26 cm

Now, the side of the rhombus is the base of the parallelogram, therefore:
h = A / s
   = 480 / 26
   = 18.46 cm

The distance between the point of intersection of the diagonals and the side of the rhombus will be: 
18.46 ÷ 2 = 9.23 cm