Question

question
which of the following sets of numbers could represent the three sides of a
triangle?
answer
{4,12,18}
{7,13,21}
{5,20,25}
{5,9,12}

Explanation:

Step1: Check triangle inequality for {4,12,18}

Check \(4 + 12>18\). \(4+12 = 16<18\). So, this set does not form a triangle.

Step2: Check triangle inequality for {5,20,25}

Check \(5 + 20>25\). \(5 + 20=25
ot>25\). So, this set does not form a triangle.

Step3: Check triangle inequality for {5,9,12}

Check \(5+9>12\) (\(14>12\)), \(5 + 12>9\) (\(17>9\)), \(9+12>5\) (\(21>5\)). All inequalities hold.

Step4: Check triangle inequality for {7,13,21}

Check \(7+13>21\). \(7 + 13=20<21\). So, this set does not form a triangle.

Answer:

\(\{5,9,12\}\)