apply the triangle inequality theorem and determine which option could be the 3rd side of a triangle if the first 2 sides measure 4 and 6.
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 measure 4 and 6.
To determine the possible values for the third side, we need to check if the sum of the first two sides is greater than the third side:
- First side = 4
- Second side = 6
4 + 6 = 10
Now, the possible values for the third side must be greater than 2 and less than 10.
Therefore, any value between 2 and 10 can be the third side of the triangle.