Apply the triangle equality theorem and determine which option could could be the third side of a triangle if the first two sides measure four and six
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.
So, to determine which option could be the third side of the triangle with sides of length four and six, we need to find the range of possible values.
For the two given sides:
4 + 6 = 10
6 - 4 = 2
Therefore, the third side must be greater than 2 and less than 10.
Options outside this range would not satisfy the triangle inequality theorem and could not be the third side of the triangle.