Question

question
which of the following sets of numbers could represent the three sides of a triangle?
answer
{11, 24, 36}
{9, 21, 28}
{13, 17, 30}
{4, 15, 20}
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Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) of a triangle, the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).

For \(\{11,24,36\}\)

• \(11+24 = 35<36\). So, this set does not form a triangle.

For \(\{9,21,28\}\)

• \(9 + 21=30<28\). So, this set does not form a triangle.

For \(\{13,17,30\}\)

• \(13+17 = 30\). Since \(13 + 17\) is not greater than \(30\), this set does not form a triangle.

For \(\{4,15,20\}\)

• \(4+15=19<20\). So, this set does not form a triangle.

Wait, there is a mistake. Let's re - check:

For \(\{11,24,36\}\)

• \(11+24 = 35<36\) (violates triangle inequality).

For \(\{9,21,28\}\)

• \(9+21 = 30>28\), \(9 + 28=37>21\), \(21+28 = 49>9\).

Answer:

\(\{9,21,28\}\)