Thank you for the opportunity to help you with your question!

The lengths of two sides of a
triangle are 12 miles and 19 miles. Which set of lengths could represent
the possible length of the third side, t?

7 miles < t < 31miles

12 miles < t < 19 miles

12 miles < t < 31 miles

7 miles < t < 19 miles

in a triangle, the sum of two smaller sides must be more than the length of the longest side.
so, if it's known that the two sides of the triangle are 12 miles and 19
miles, and the third side t is unknown, then there are 2 possibilities:

1. t is the longest side, therefore:
12 + 19 > t
31 > t
2. t is the shortest side, therefore:
t + 12 > 19
t > 19 - 12

t > 7

Therefore,the answer will be : 7 miles < t < 31 miles

Please let me know if you need any clarification. I'm always happy to answer your questions.