Question

determine if three given side lengths can form a triangle. find the range of possible values if one side length of a triangle is unknown. value: 5 the sides lengths 4, 6, 9 can be used to form the sides of a triangle. true false

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

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

Step3: Check the second inequality

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

Step4: Check the third inequality

\(b + c=6 + 9=15\), and \(15>4\) (i.e., \(b + c>a\)).

Answer:

A. True