Question

which of the following sets of numbers could represent the three sides of a triangle? answer {7,10,19} {6,21,29} {7,13,21} {9,23,29}

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 {7,10,19}

\(7+10 = 17<19\), so it cannot form a triangle.

Step3: Check {6,21,29}

\(6 + 21=27<29\), so it cannot form a triangle.

Step4: Check {7,13,21}

\(7+13 = 20>21\), \(7 + 21=28>13\), \(13+21 = 34>7\), so it can form a triangle.

Step5: Check {9,23,29}

\(9+23 = 32>29\), \(9 + 29=38>23\), \(23+29 = 52>9\), but we already found the correct set in Step 4.

Answer:

{7,13,21}