Question

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Question
Can the side lengths of a triangle be 3, 6 and 9? (1 point)
Responses

yes
yes

no
no

Answer 1

To determine if the side lengths 3, 6, and 9 can form a triangle, 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.

Let's check all three combinations for the given sides:

1. \(3 + 6 > 9\) (9 is not greater than 9, so this fails)
2. \(3 + 9 > 6\) (12 > 6, this is true)
3. \(6 + 9 > 3\) (15 > 3, this is true)

Since one of the conditions (3 + 6 > 9) does not hold, the side lengths 3, 6, and 9 cannot form a triangle.

The correct response is **no**.