79.2k views
5 votes
Given three side lengths 9, 13, and 19:

Complete the following statements, using:

I. 9 + 13 = 19
II. 9 + 19 = 13
III. 13 + 19 = 9

A) I, II, III
B) I, III
C) II, III
D) I, II

1 Answer

4 votes

Final answer:

None of the statements I, II, or III are true because each set of side lengths violates the triangle inequality theorem.

Step-by-step explanation:

The question is about triangle inequality, 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. Looking at the given side lengths of 9, 13, and 19, we can see that:

  • 9 + 13 = 22, which is greater than 19
  • 9 + 19 = 28, which is greater than 13
  • 13 + 19 = 32, which is greater than 9

Therefore, none of the statements I, II, or III are true. They would imply that you can have sides of a triangle which don't adhere to the triangle inequality, but in fact, all sets of side lengths given must obey the triangle inequality for a triangle to exist.

User Ebaynaud
by
8.1k 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