Which of the following lists of three numbers could form the side lengths of a triangle? A. $10, 20, 30$B. $122, 257, 137$C. $8.6, 12.2, 2.7$D. $(1)/(2), (1)/(5), (1)/(6)$

Question

Which of the following lists of three numbers could form the side lengths of a triangle?
`A. $10, 20, 30$B. $122, 257, 137$C. $8.6, 12.2, 2.7$D. $(1)/(2), (1)/(5), (1)/(6)$`

Answer 1

B. 122, 257, 137

Explanation:

The triangle inequality rule states that the sum of any two sides of a triangle must be greater than the third side. If A, B and C are sides of a triangle then A + B > C, A + C > B, B + C > A

Testing for the options:

1) 10, 20, 30

10 + 20 (= 30) is not greater than 30. It cannot form a triangle

2) 122, 257, 137

122 + 137 (259) is greater than 257. It can form a triangle

3) 8.6, 12.2, 2.7

8.6 + 2.7 (11.3) is not greater than 12.2. It cannot form a triangle

4) 1/2, 1/5, 1/6

1/5 + 1/6 (11//30) is not greater than 1/2. It cannot form a triangle