Question

Which of the following number sets could not represent the three sides of a triangle?

{6, 18,23} {8, 10, 20}
{13, 16, 26} {6, 14, 19}

Answer 1

The set {8, 10, 20} cannot represent the sides of a triangle because the sum of the lengths of any two sides must be greater than the length of the third side, as stated by the Triangle Inequality Theorem, and 8 + 10 is not greater than 20. The correct answer is option: {8, 10, 20}

Step-by-step explanation:

The question is asking which set of three numbers cannot represent the sides of a triangle. To determine this, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We will apply this theorem to each set to find which one cannot represent a triangle.

• {6, 18, 23}: The sum of the smallest two numbers, 6 + 18 = 24, which is greater than 23. Hence, these can represent the sides of a triangle.
• {8, 10, 20}: The sum of the smallest two numbers, 8 + 10 = 18, which is not greater than 20. Thus, these numbers cannot represent the sides of a triangle.
• {13, 16, 26}: The sum of the smallest two numbers, 13 + 16 = 29, which is greater than 26. Therefore, these can represent the sides of a triangle.
• {6, 14, 19}: The sum of the smallest two numbers, 6 + 14 = 20, which is greater than 19. Thus, these numbers can represent the sides of a triangle.

The set {8, 10, 20} cannot represent the sides of a triangle because it does not satisfy the Triangle Inequality Theorem.