Question

can a triangle be formed with side lengths 3, 9, 17? explain.
no, because 3 + 9 < 17
yes, because 3 + 9 > 17
no, because 17 − 3 < 9
yes, because 17 − 9 < 3

Explanation:

Step1: Check triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let \(a = 3\), \(b = 9\), and \(c = 17\).
First, check \(a + b>c\): \(3+9 = 12\), and \(12<17\).

Step2: Analyze other inequalities (optional for this case)

Even if we check \(a + c>b\) (\(3 + 17=20>9\)) and \(b + c>a\) (\(9+17 = 26>3\)), since \(3 + 9<17\) fails the triangle - inequality theorem.

Answer:

No, because \(3 + 9<17\)