Question

which numbers could represent the lengths of the sides of a triangle?
1, 2, 4
3, 6, 8
7, 7, 15
5, 9, 14

Explanation:

Step1: Check triangle inequality theorem

For three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), the triangle inequality theorem states that \(a + b>c\).

Step2: Analyze option \(1,2,4\)

Here \(a = 1\), \(b=2\), \(c = 4\). Then \(a + b=1 + 2=3<4\), so these cannot form a triangle.

Step3: Analyze option \(3,6,8\)

Here \(a = 3\), \(b = 6\), \(c=8\). Then \(a + b=3+6 = 9>8\).

Step4: Analyze option \(7,7,15\)

Here \(a = 7\), \(b = 7\), \(c=15\). Then \(a + b=7 + 7=14<15\), so these cannot form a triangle.

Step5: Analyze option \(5,9,14\)

Here \(a = 5\), \(b = 9\), \(c=14\). Then \(a + b=5 + 9=14\), and \(a + b\) is not greater than \(c\) (it is equal), so these cannot form a triangle.

Answer:

\(3,6,8\)