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.8B.24C.2D.5E.19F.10

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 other two sides and greater than the absolute difference of the other two sides. This is known as the triangle inequality theorem.

Given sides of lengths 5 and 13:

• The sum of the two sides is 5 + 13 = 18.
• The absolute difference 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. 8 - This is equal to the absolute difference, not greater. So, it does not apply. B. 24 - This is greater than the sum of the other two sides. So, it does not apply. C. 2 - This is less than the absolute difference. So, it does not apply. D. 5 - This is less than the sum and greater than the absolute difference. So, it applies. E. 19 - This is greater than the sum of the other two sides. So, it does not apply. F. 10 - This is less than the sum and greater than the absolute difference. So, it applies.

So, the possible lengths for the third side could be 5 (D) and 10 (F).