Apply the triangle inequality theorem, and determine which option could be the third side of a triangle as the first two sides measure 4 and 6
According to the triangle inequality theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that the first two sides measure 4 and 6, to form a triangle, the third side must satisfy the following condition:
4 + 6 > x (where x is the length of the third side)
Therefore, the third side (x) must be less than the sum of the first two sides, which is 10.
So, any option that is less than 10 could be the third side of a triangle with sides measuring 4 and 6.