What is the longest possible side length that is an integer of a triangle whose two shorter sides are 15 and 21?

Answer 1

Third side must be less than the sum of the other two.

x < 15 + 21

x < 36

Answer 2

any side is less than the sum of the other two sides

any side is greater than the difference of the other two sides

21-15 < Third Side < 21+15

6 < T < 36

35 is the largest integer for the Third Side

at 36, the triangle degenerates or collapses into a straight line

at 37, there is no triangle