How can inequalities be related to and solve problems with triangles?

Question

How can inequalities be related to and solve problems with triangles?

Answer 1

If the side lengths of a triangle are a, b, and c, and a > b > 0, a > c > 0 (i.e., a is the longest side);

then the following must be true to make a triangle: b + c > a.

Otherwise the ends either wouldn't meet or the segments would be collinear.

 

Which of the following sets would make triangles and why?

 

(a, b, c):

(10,6,7)

(5,11,6)

(9,13,3)