A triangle has two sides of lengths 5 and 13. What value could the length of the third side be? Check all that apply.A.19B.10C.8D.5E.24F.2

The length of the third side of a triangle, given the lengths of the other two sides, must be less than the sum of the lengths of the other two sides and greater than the absolute difference of the lengths of the other two sides. This is known as the triangle inequality theorem.

Given sides of lengths 5 and 13:

• The sum of the lengths of the two sides is 5 + 13 = 18.
• The absolute difference of the lengths of the two sides is |5 - 13| = 8.

Therefore, the length of the third side must be greater than 8 and less than 18.

Checking the options:

A. 19 - This is greater than 18, so it is not possible. B. 10 - This is between 8 and 18, so it is possible. C. 8 - This is equal to the absolute difference, so it is possible. D. 5 - This is less than 8, so it is not possible. E. 24 - This is greater than 18, so it is not possible. F. 2 - This is less than 8, so it is not possible.

So, the possible lengths for the third side are 10 and 8 (Options B and C).