Two sides of a triangle are 10 cm and 5 cm. Determine the length of the third side from the choices given.
Since the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, the third side must be greater than the difference between the other two sides and smaller than their sum.
Therefore, the third side must be greater than 10 - 5 = 5 cm and smaller than 10 + 5 = 15 cm.
Therefore, the possible lengths for the third side are between 5 cm and 15 cm.