Question

In ΔАВC, the correct relation is ______.

Options

• AB – BC > CA

• BC – CA > AB

• AB + BC < AC

• AB < BC + AC

Answer 1

In ΔАВC, the correct relation is AB < BC + AC.

Explanation:

By the triangle inequality,

The sum of any two sides of a triangle is greater than the third side. 

Therefore, AB < BC + AC.

Why the others are wrong (brief):

1. AB – BC > CA would imply AB > BC + CA, contradicting the triangle inequality.
2. BC – CA > AB would imply BC > CA + AB, also impossible.
3. AB + BC < AC directly contradicts the triangle inequality it says the sum of two sides is less than the third.