Why triangle inequality is so damn important!
Triangle inequality is an important triangle property that is *very* frequently tested on the GRE. Remember this:
The sum of the lengths of any two sides of a triangle is always greater than the length of its third side.
The above figure shows with sides , and as shown. Based on what we just learnt, all of the following inequalities are true:
It two sides of a triangle are 5 cm and 6 cm respectively, which of the following can NOT be a value of the third side?
A) 2 cm
B) 5 cm
C) 6 cm
D) 10 cm
E) 11 cm
The third side has to be less than the sum, and more than the difference of 5 and 6. Therefore the third side must be less than 11 and more than 1.
Thus 11 CM cannot be the length of the third side.
E is the right answer.