Two sides of a triangle have lengths of 10 and 13. The length of the third side can be any number between _________ and ________.

13-10 < x < 13+10

To determine the possible range for the length of the third side of a triangle given two side lengths, we need to apply the triangle inequality theorem. According to this 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 two given sides have lengths of 10 and 13. So, we can apply the triangle inequality theorem to find the range of possible values for the length of the third side.

To find the maximum possible length of the third side, we add the lengths of the two given sides together and subtract the smaller side length from the sum:
Maximum Length = 10 + 13 - 10 = 23

To find the minimum possible length of the third side, we subtract the length of the larger given side from the length of the other side:
Minimum Length = 13 - 10 = 3

Therefore, the length of the third side can be any number between 3 and 23.