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Question

Question
Can the sides of a triangle have lengths 6, 14, 18. Remember to use the Triangle Inequality Theorem.

Remember:

(1 point)
Responses

Yes
Yes

No

Answer 1

To determine if the sides of a triangle can have lengths 6, 14, and 18, we can use the Triangle Inequality Theorem. This theorem states that, for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following must hold true:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's define the sides as follows:

• \(a = 6\)
• \(b = 14\)
• \(c = 18\)

Now we can check the inequalities:

1. \(6 + 14 > 18\)
   \(20 > 18\) (True)

2. \(6 + 18 > 14\)
   \(24 > 14\) (True)

3. \(14 + 18 > 6\)
   \(32 > 6\) (True)

Since all three conditions of the Triangle Inequality Theorem are satisfied, the lengths 6, 14, and 18 can indeed form a triangle.

Response: Yes