A triangle has two sides of length 16 and 14. What is the largest possible whole-number length for the third side?

This is easily solved by looking at the extreme case. For any triangle with sides a, b, and c, the sum of the length of ANY two sides MUST be less than the length of the third side. This is obvious if you try to make the length of the third side equal to the sum of the length of the other two sides. If you make the length of the third side the sum of the length of the other two sides you have a line segment, not a triangle.

In this case the sum of the length of the two sides is 16 + 14 = 30. Therefore we know that the length of the third side can be less than 30. If we restrict ourselves to whole numbers, the largest whole number less than 30 is 29.

Also note that the third side must be LARGER than 16 - 14 = 2. Can you figure out why?

The largest possible whole-number length for the third side of the triangle is 29.