Question

question: which of the following sets of numbers could represent the three sides of a triangle? answer: {5,15,22} {8,22,32} {14,17,28} {13,21,34}

Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

Step2: Check set {5, 15, 22}

\(5+15 = 20<22\), so it cannot form a triangle.

Step3: Check set {8, 22, 32}

\(8 + 22=30<32\), so it cannot form a triangle.

Step4: Check set {14, 17, 28}

\(14+17 = 31>28\), \(14 + 28=42>17\), \(17+28 = 45>14\), so it can form a triangle.

Step5: Check set {13, 21, 34}

\(13+21 = 34\), and for a triangle \(a + b\) must be strictly greater than \(c\), so it cannot form a triangle.

Answer:

C. {14, 17, 28}