Answer:
14
Step-by-step explanation:
The triangle inequality is usually expressed as ...
a +b > c
for any permutation of a, b, c.
Here, that would mean ...
1 + 14 > c
c < 15
The largest whole-number value that the third side (c) can have is 14.
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Additional comments
Some authors write the triangle inequality as ...
a +b ≥ c
If you use that version, the longest side could be 15. Such a "triangle" would look like a line segment, and have zero area.
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We can also check the shortest length:
c +1 > 14
c > 13
The smallest whole-number value for the shortest side is also 14. That is, the only triangle with whole-number side lengths of 1 and 14 will be an isosceles triangle with two sides of length 14.
