Question

value: 5
the sides lengths 4, 6, 9 can be used to form the sides of a triangle.
true
false

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Explanation:

Step1: Recall triangle - inequality theorem

For three side - lengths \(a\), \(b\), and \(c\) of a triangle, the following three inequalities must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\).
Let \(a = 4\), \(b = 6\), and \(c = 9\).

Step2: Check the first inequality

\(a + b=4 + 6=10>9\) (i.e., \(a + b>c\)).

Step3: Check the second inequality

\(a + c=4 + 9 = 13>6\) (i.e., \(a + c>b\)).

Step4: Check the third inequality

\(b + c=6+9 = 15>4\) (i.e., \(b + c>a\)).
Since all three inequalities hold, the side - lengths 4, 6, and 9 can form a triangle.

Answer:

True