Question

which of the following sets of numbers could represent the three sides of a triangle?
answer
{6,14,21} {8,12,18}
{6,10,16} {9,16,25}

Explanation:

Step1: Recall triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leqslant b\leqslant c\)), the sum of the two shorter sides \(a + b>c\).

Step2: Check set \(\{6,14,21\}\)

Here \(a = 6\), \(b=14\), \(c = 21\). Then \(a + b=6 + 14=20\), and \(20<21\). So this set does not form a triangle.

Step3: Check set \(\{8,12,18\}\)

Here \(a = 8\), \(b = 12\), \(c=18\). Then \(a + b=8+12 = 20\), and \(20>18\).

Step4: Check set \(\{6,10,16\}\)

Here \(a = 6\), \(b = 10\), \(c=16\). Then \(a + b=6 + 10=16\), and \(16 = 16\) (not \(>\)). So this set does not form a triangle.

Step5: Check set \(\{9,16,25\}\)

Here \(a = 9\), \(b = 16\), \(c=25\). Then \(a + b=9+16 = 25\), and \(25=25\) (not \(>\)). So this set does not form a triangle.

Answer:

\(\{8,12,18\}\)