Question 756299
hello,

By the triangle inequality, the sum of the lengths of the two sides of a triangle must be more than the length of the third side. 

We are trying to minimize t, so it is safe to say that the minimum of t exists when the side with length 19 is the longest side. 

We get t+t>19 from the triangle inequality, so 2t>19, so t>9.5, 

Since t is an integer, the smallest possible integer value of t is 10. 

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