Question

Apply the Triangle Inequality Theorem to determine whether sides with lengths of 5 inches, 10 inches, and 15 inches form a triangle.(1 point) Responses Yes, because the sum of 5+10 is not greater than 15. Yes, because the sum of 5 plus 10 is not greater than 15. Yes, the majority of the conditions are met. Yes, the majority of the conditions are met. No, because the sum of 5+10 is not greater than 15. No, because the sum of 5 plus 10 is not greater than 15. Yes, because the sum of 5+10 is less than or equal to 15.

Answer 1

To determine if the sides with lengths of 5 inches, 10 inches, and 15 inches can form a triangle, we can apply the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

We need to check the following conditions:

1. \(5 + 10 > 15\)
2. \(5 + 15 > 10\)
3. \(10 + 15 > 5\)

Now, let's evaluate each of these:

1. \(5 + 10 = 15\) (not greater than 15)
2. \(5 + 15 = 20\) (greater than 10)
3. \(10 + 15 = 25\) (greater than 5)

The first condition is not satisfied because \(5 + 10\) is equal to 15, not greater. Therefore, these lengths do not satisfy the Triangle Inequality Theorem and cannot form a triangle.

Based on this evaluation, the correct response would be:

No, because the sum of 5 plus 10 is not greater than 15.