Question

Which of the following sets of numbers could NOT represent the three sides of a triangle?

{8, 20, 26} {8, 20, 27}
{13, 20, 30} {10, 16, 27}

Answer 1

{10, 16, 27}

Explanation:

The longest side of the triangle is greater than the sum of the other two sides, so it cannot be a triangle.

Answer 2

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's check each set:

1. {8, 20, 26} - This set satisfies the triangle inequality (8 + 20 > 26, 8 + 26 > 20, 20 + 26 > 8).

2. {8, 20, 27} - This set satisfies the triangle inequality (8 + 20 > 27, 8 + 27 > 20, 20 + 27 > 8).

3. {13, 20, 30} - This set satisfies the triangle inequality (13 + 20 > 30, 13 + 30 > 20, 20 + 30 > 13).

4. {10, 16, 27} - This set does not satisfy the triangle inequality (10 + 16 = 26, which is not greater than 27).

Therefore, the set {10, 16, 27} could NOT represent the three sides of a triangle.