Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12?
A) 15
B) 22
C) 30
D) 24
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the first two sides have lengths of 10 and 12. The third side must be greater than the difference between these two sides and less than the sum of these two sides. The difference between 12 and 10 is 2, and the sum of 12 and 10 is 22.
Therefore, the length of the third side must be greater than 2 and less than 22. Only one of the given choices falls within this range, which is 15.
The length of the third side is 15.
Therefore, the correct answer is A) 15.