Question

Which of the following lists of three numbers could form the side lengths of a triangle? %2410%2C%2020%2C%2030%24B.%20%24122%2C%20257%2C%20137%24C.%20%248.6%2C%2012.2%2C%202.7%24D.%20%24%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B1%7D%7B5%7D%2C%20%5Cfrac%7B1%7D%7B6%7D%24" id="TexFormula1" title="A. $10, 20, 30$B. $122, 257, 137$C. $8.6, 12.2, 2.7$D. $\frac{1}{2}, \frac{1}{5}, \frac{1}{6}$" alt="A. $10, 20, 30$B. $122, 257, 137$C. $8.6, 12.2, 2.7$D. $\frac{1}{2}, \frac{1}{5}, \frac{1}{6}$" align="absmiddle" class="latex-formula">

Answer 1

Answer:

B. 122, 257, 137

Step-by-step 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