Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {6,16,19} {4,19,25} {14,18,30} {4,11,13}

Explanation:

Step1: Recall the triangle inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check the set \(\{4,19,25\}\)

• \(4 + 19=23\)
• Since \(23<25\), the sum of the two shorter sides (\(4\) and \(19\)) is not greater than the longest side (\(25\)).

Step3: Check other sets for completeness (optional but good practice)

• For \(\{6,16,19\}\): \(6 + 16=22>19\), \(6+19 = 25>16\), \(16 + 19=35>6\)
• For \(\{14,18,30\}\): \(14+18 = 32>30\), \(14 + 30=44>18\), \(18+30 = 48>14\)
• For \(\{4,11,13\}\): \(4+11=15>13\), \(4 + 13=17>11\), \(11+13=24>4\)

Answer:

\(\{4,19,25\}\)