Question

which of the following sets of numbers could not represent the three sides of a triangle?
answer
{4,16,17} {15,24,36}
{14,26,37} {12,24,37}

Explanation:

Step1: Recall the triangle inequality theorem

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

Step2: Check each set

• Set \(\{4,16,17\}\):

\(4 + 16=20>17\)

• Set \(\{15,24,36\}\):

\(15 + 24 = 39>36\)

• Set \(\{14,26,37\}\):

\(14+26 = 40>37\)

• Set \(\{12,24,37\}\):

\(12+24=36<37\)

Answer:

\(\{12,24,37\}\)