We can use the triangle inequality theorem to test each set of numbers. This theorem states that if the sides of a triangle are A, B, and C, then A+B>C, B+C>A, A+C>B. Otherwise, any two given sides must add to be greater then the third side.
A)
3+4>8
4+8>3
3+8>4
The second and third statements are false, therefore this cannot be a triangle.
B)
16+19>20
19+20>16
16+20>19
All of these statements are true, this can be a triangle.
C)
8+11>19
11+19>8
8+19>11
The first statement of this set is not true, therefore this set cannot be a triangle.
D)
11+5>5
5+5>11
11+5>5
The second statement of this set is not true, therefore this set cannot be a triangle.
From the calcuations above, its clear that the answer is B.
