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 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. Yes, because the sum of 5 plus 10 is less than or equal to 15. Yes, the majority of the conditions are met. Yes, the majority of the conditions are met. Yes, because the sum of 5+10 is not greater than 15.

Answer 1

To determine whether the lengths of 5 inches, 10 inches, and 15 inches can form a triangle, we apply the Triangle Inequality Theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold:

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

In this case, we have sides of lengths 5, 10, and 15. Let's label them as follows:
- \(a = 5\)
- \(b = 10\)
- \(c = 15\)

Now we can check the conditions:

1. \(5 + 10 > 15\) → \(15 > 15\) (not satisfied)
2. \(5 + 15 > 10\) → \(20 > 10\) (satisfied)
3. \(10 + 15 > 5\) → \(25 > 5\) (satisfied)

Since the first condition is not satisfied (the sum is not greater than 15), the lengths 5 inches, 10 inches, and 15 inches do not satisfy the Triangle Inequality Theorem.

Therefore, the answer is:

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