Final answer:
The length of the other diagonal of the rhombus cannot be determined.
Step-by-step explanation:
A rhombus is a quadrilateral with all four sides of equal length. In a rhombus, the diagonals are perpendicular bisectors of each other.
Given that the length of each side of the rhombus is 10 cm, and one of its diagonals is 16 cm, we can use the Pythagorean theorem to find the length of the other diagonal.
Let's call the length of the other diagonal x. Using the Pythagorean theorem, we have:
10^2 = (x/2)^2 + 16^2
100 = x^2/4 + 256
x^2/4 = 100 - 256
x^2/4 = -156
x^2 = -624
Since the measurement of a length cannot be negative, we can conclude that the length of the other diagonal is not a real number. Therefore, there is no length for the other diagonal.