Question

The lengths of three sides of a triangle are m units, n units, and p units, respectively. Which inequality must be true?

A) m > n + p

B) n < m + p

C) p > m + n

D) p < m – n

Answer 1

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the inequality that must be true is n < m + p.

Answer 2

n < m + p

Explanation:

If ABC is a triangle then the sum of any two sides of ABC will be greater than the third side i.e. AB + BC > CA or BC + CA > AB or CA + AB > BC.

Now, if the lengths of three sides of a triangle are m units, n units, and p units respectively.

Then the inequality must be true is n < m + p, where m + p is the sum of any two sides which is greater than the third side of n length. (Answer)