Question

which set of side lengths does not form a triangle? 39, 80, 89 14, 15, 29 36, 77, 85 16, 63, 65

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\)

Step2: Check each set

• Set \(39,80,89\):

\(39+80 = 119>89\)

• Set \(14,15,29\):

\(14 + 15=29\), and \(29
ot>29\)

• Set \(36,77,85\):

\(36+77=113>85\)

• Set \(16,61,65\):

\(16 + 61=77>65\)

Answer:

\(14,15,29\)