applying the triangle inequality theorem determine which option could be the third side of a triangle if the first two sides measure 4 and 6
To determine if a given length can be the third side of a triangle when the first two sides measure 4 and 6, we can apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using this theorem, we can check if the given length could be the third side of a triangle:
1. If the third side is 2, then 4 + 6 > 2, which is true. So, the third side of 2 could be a possible side length for the triangle.
2. If the third side is 8, then 4 + 6 > 8, which is not true. So, the third side of 8 cannot be a side length for the triangle.
Therefore, the third side of a triangle can be 2 units long if the first two sides measure 4 and 6.