we know that
The triangle inequality theorem states that : Any side of a triangle must be shorter than the other two sides added together
so
Verify the theorem in each case
Part 1) 3,4,5
we have that
3 < 4+5
3 <9 ----> is ok
4 < 3+5
4 < 8 ----> is ok
5 < 3+4
5 <7 ----> is ok
therefore
the three numbers can be the side lengths of a triangle
Part 2) we have
3,7,10
10 < 3+7
10 < 10 ----> is not true
therefore
the three numbers can not be the side lengths of a triangle
Part 3)
we have
6.2, 7.9, 12.5
12.5 < 6.2+7.9
12.5 < 14.10 ---> is ok
6.2 < 7.9+12.5 ----> is ok
7.9 < 6.2+12.5 ----> is ok
therefore
the three numbers can be the side lengths of a triangle
Part 4
we have
2,8,9
9 < 2+8 ----> is ok
2 < 8+9 ----> is ok
8 < 2+9 ----> is ok
therefore
the three numbers can be the side lengths of a triangle
Part 5
we have
10,20,50
50 < 10+20 ------> is not ok
therefore
the three numbers can not be the side lengths of a triangle