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 a triangle can have sides of lengths 6, 14, and 18, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. We need to check all three conditions:

1. \(6 + 14 > 18\)
2. \(6 + 18 > 14\)
3. \(14 + 18 > 6\)

Now, let's calculate:

1. \(6 + 14 = 20\), which is greater than \(18\) (True).
2. \(6 + 18 = 24\), which is greater than \(14\) (True).
3. \(14 + 18 = 32\), which is greater than \(6\) (True).

Since all three conditions of the Triangle Inequality Theorem hold true, the sides can indeed form a triangle.

The response is: **Yes**.