Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {8,20,27} {8,19,25} {13,20,32} {6,8,16}

Explanation:

Step1: Recall the triangle inequality theorem

For three side lengths \(a\), \(b\), and \(c\) (\(a\leq b\leq c\)), the sum of the two shorter sides \(a + b\) must be greater than the longest side \(c\).

Step2: Check the set \(\{8,20,27\}\)

Here \(a = 8\), \(b=20\), \(c = 27\). Calculate \(a + b=8 + 20=28\). Since \(28>27\), this set can form a triangle.

Step3: Check the set \(\{8,19,25\}\)

Here \(a = 8\), \(b = 19\), \(c=25\). Calculate \(a + b=8+19 = 27\). Since \(27>25\), this set can form a triangle.

Step4: Check the set \(\{13,20,32\}\)

Here \(a = 13\), \(b = 20\), \(c=32\). Calculate \(a + b=13 + 20=33\). Since \(33>32\), this set can form a triangle.

Step5: Check the set \(\{6,8,16\}\)

Here \(a = 6\), \(b = 8\), \(c=16\). Calculate \(a + b=6 + 8=14\). Since \(14<16\), this set cannot form a triangle.

Answer:

\(\{6,8,16\}\)