Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two 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, we have two sides measuring 4 and 6. To determine if a third side could be part of a triangle, we need to check if the sum of the two given sides is greater than the length of the potential third side.
If we let the third side be x, the inequality we need to check is:
4 + 6 > x
10 > x
So, any side length greater than 10 would satisfy the Triangle Inequality Theorem and could be the third side of a triangle.