Question

8
which set of numbers can represent the lengths of the sides of a triangle?
{3,5,7}
{4,4,8}
{3,9,14}
{1,2,3}

Explanation:

Step1: Check triangle inequality for {3,5,7}

Check \(3 + 5>7\) (\(8>7\)), \(3 + 7>5\) (\(10>5\)), \(5 + 7>3\) (\(12>3\))

Step2: Check triangle inequality for {4,4,8}

Check \(4+4 = 8\), which does not satisfy \(a + b>c\) (triangle inequality)

Step3: Check triangle inequality for {3,9,14}

Check \(3+9=12<14\), which does not satisfy \(a + b>c\) (triangle inequality)

Step4: Check triangle inequality for {1,2,3}

Check \(1 + 2=3\), which does not satisfy \(a + b>c\) (triangle inequality)

Answer:

\(\{3,5,7\}\)