Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {7,21,25} {5,18,20} {8,13,19} {15,20,37} submit answer

Explanation:

Step1: Check triangle inequality for {7,21,25}

Check if \(7 + 21>25\), \(7+25 > 21\), \(21 + 25>7\).
\(7+21 = 28>25\), \(7 + 25=32>21\), \(21+25 = 46>7\).

Step2: Check triangle inequality for {5,18,20}

Check if \(5+18>20\), \(5 + 20>18\), \(18+20>5\).
\(5+18=23>20\), \(5+20 = 25>18\), \(18+20=38>5\).

Step3: Check triangle inequality for {8,13,19}

Check if \(8+13>19\), \(8+19>13\), \(13+19>8\).
\(8 + 13=21>19\), \(8+19=27>13\), \(13+19=32>8\).

Step4: Check triangle inequality for {15,20,37}

Check if \(15+20>37\), \(15+37>20\), \(20+37>15\).
\(15+20=35<37\).

Answer:

\(\{15,20,37\}\)