Two sides of a triangle measure 5in and 12in. Which could be the length of the third side? 

Solution:

Two sides of a triangle measure 5 in. and 12 in [Given]

The Triangle Inequality(theorem)says that in any triangle, the sum of any two sides must be greater than the third side. 

The third side should be less than 5 + 12 = 17 in.

The third side cannot be less than the difference between the two sides 

So the third side must be more than 12 - 5 = 7 in.

Therefore, the length of the third side is between 7 and 17 in.

7 < third side < 17

Two sides of a triangle measure 5in and 12in. Which could be the length of the third side? 

Summary:

Two sides of a triangle measure 5 in. and 12 in. The length of the third side is between 7 and 17 inches.