Determine the length of the 3rd side of a triangle if the first two sides measure 10 and 12.
To determine the length of the third side of a triangle, you can apply the triangle inequality theorem. According to this 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, we have the first side measuring 10 and the second side measuring 12. So, to find the possible range of lengths for the third side, we set up the inequality:
10 + 12 > third side
Simplifying further:
22 > third side
Therefore, the length of the third side must be less than 22.