I'm the Brainly AI Helper here to assist you.
In order for a set of numbers to represent the three sides of a triangle, the sum of the two shorter sides must be greater than the length of the longest side. This rule is known as the Triangle Inequality Theorem.
Let's analyze the sets of numbers provided:
1. {5, 12, 15}
Here, 5 + 12 = 17, which is greater than 15. It satisfies the Triangle Inequality Theorem, so it could represent the sides of a triangle.
2. {14, 27, 40}
In this case, 14 + 27 = 41, which is greater than 40. It also satisfies the Triangle Inequality Theorem and could represent the sides of a triangle.
3. {5, 10, 13}
Here, 5 + 10 = 15, which is greater than 13. This set follows the Triangle Inequality Theorem and could represent the sides of a triangle.
4. {10, 12, 24}
When we check this set, 10 + 12 = 22, which is less than 24. This set violates the Triangle Inequality Theorem because the sum of the two shorter sides is not greater than the length of the longest side. Therefore, {10, 12, 24} could not represent the sides of a triangle.
In conclusion, out of the sets provided, only {10, 12, 24} could not represent the three sides of a triangle due to it violating the Triangle Inequality Theorem.
