Question

which set of numbers can represent the lengths of the sides of a triangle?
{4,4,9}
{3,3,6}
{4,7,10}
{3,4,7}

Explanation:

Step1: Check triangle inequality for {4,4,9}

Check \(4 + 4>9\). Since \(4+4 = 8<9\), this set does not form a triangle.

Step2: Check triangle inequality for {3,3,6}

Check \(3 + 3>6\). Since \(3 + 3=6\), this set does not form a triangle (inequality is strict \(a + b>c\)).

Step3: Check triangle inequality for {4,7,10}

Check \(4+7>10\) (\(11>10\)), \(4 + 10>7\) (\(14>7\)), \(7+10>4\) (\(17>4\)). All inequalities hold.

Step4: Check triangle inequality for {3,4,7}

Check \(3 + 4>7\). Since \(3+4 = 7\), this set does not form a triangle (inequality is strict \(a + b>c\)).

Answer:

\(\{4,7,10\}\)