Apply the triangle inequality theorem and determine which option could be the third side of a triangle in the first two sides measure 4 and 6
To determine if a third side can form a triangle with sides measuring 4 and 6, we need to apply 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.
Let's denote the third side as x.
So, according to the triangle inequality theorem, we have:
4 + 6 > x
10 > x
This means that the third side must be less than the sum of the other two sides. Therefore, any option for the third side that is less than 10 would work. For example, a third side of 8 would be valid, as 4 + 6 > 8 (10 > 8).
Therefore, any third side less than 10 could be a valid option for forming a triangle with sides measuring 4 and 6.