Question

do the following side lengths create a triangle? 15, 12, 9 no clue sometimes no yes

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for three side lengths \(a\), \(b\), and \(c\) to form a triangle, the sum of any two sides must be greater than the third side. Mathematically, this means:
\(a + b > c\), \(a + c > b\), and \(b + c > a\).

Step2: Check the given side lengths

Let \(a = 15\), \(b = 12\), and \(c = 9\).

• Check \(a + b > c\): \(15 + 12 = 27\), and \(27 > 9\).
• Check \(a + c > b\): \(15 + 9 = 24\), and \(24 > 12\).
• Check \(b + c > a\): \(12 + 9 = 21\), and \(21 > 15\).

Since all three conditions of the triangle inequality theorem are satisfied, the side lengths \(15\), \(12\), and \(9\) can form a triangle.

Answer:

Yes (The option corresponding to "Yes" in the green box)