Final answer:
The possible length of the third side of the triangle, given the other two side lengths of 4 and 6, can be any number less than 10.
Step-by-step explanation:
To find the possible length of the third side of a triangle, given the other two side lengths of 4 and 6, we can use the Triangle Inequality Theorem. According to this theorem, the sum of the two smaller side lengths of a triangle must be greater than the length of the third side.
In this case, we have side lengths of 4 and 6. To find the possible length of the third side, we need to determine the range of values that satisfy the inequality 4 + 6 > x, where x represents the length of the third side. Simplifying the inequality, we get 10 > x. Therefore, the third side length can be any number less than 10.
So, the possible lengths of the third side of the triangle can be any number less than 10.