175k views
3 votes
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}

2 Answers

2 votes

Answer:

{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.

User Andrea Gherardi
by
8.2k points
5 votes

Answer:

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.

User AVokin
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories