Question

which of the following sets of numbers could represent the three sides of a triangle? answer {12,17,30} {6,19,22} {11,21,33} {13,22,35} submit answer

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check {12, 17, 30}

\(12+17 = 29<30\), so it cannot form a triangle.

Step3: Check {6, 19, 22}

\(6 + 19=25>22\), \(6+22 = 28>19\), \(19 + 22=41>6\), so it can form a triangle.

Step4: Check {11, 21, 33}

\(11+21 = 32<33\), so it cannot form a triangle.

Step5: Check {13, 22, 35}

\(13+22 = 35\), and for a triangle \(a + b\) must be strictly greater than \(c\), so it cannot form a triangle.

Answer:

{6, 19, 22}