Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {11,17,26} {10,14,25} {14,26,38} {11,13,23}

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 \(\{10,14,25\}\)

• \(10 + 14=24\)
• Since \(24<25\), the triangle inequality theorem is violated.

Step3: Check the set \(\{11,17,26\}\)

• \(11+17 = 28>26\)
• \(11 + 26=37>17\)
• \(17+26 = 43>11\)

Step4: Check the set \(\{14,26,38\}\)

• \(14+26=40>38\)
• \(14 + 38=52>26\)
• \(26+38=64>14\)

Step5: Check the set \(\{11,13,23\}\)

• \(11+13=24>23\)
• \(11+23 = 34>13\)
• \(13+23=36>11\)

Answer:

\(\{10,14,25\}\)