The sum of the lengths of any kind of two sides of a triangle is better than the length of the third side.

In the figure, the complying with inequalities hold.

a + b > c

a + c > b

b + c > a

** instance 1: **

check whether the is possible to have actually a triangle through the given side lengths.

7 , 9 , 13

add any two sides and see if it is higher than the other side.

The sum of 7 and also 9 is 16 and also 16 is higher than 13 .

The amount of 9 and 13 is 21 and also 21 is higher than 7 .

The sum of 7 and 13 is 20 and also 20 is better than 9 .

This set of side lengths satisfies the Triangle Inequality Theorem.

this lengths do kind a triangle.

** instance 2: **

inspect whether the provided side lengths type a triangle.

4 , 8 , 15

check whether the sides accomplish the Triangle Inequality Theorem.

add any 2 sides and also see if that is better than the other side.

The amount of 4 and also 8 is 12 and also 12 is much less than 15 .

This set of side lengths walk not satisfy Triangle Inequality Theorem.

this lengths carry out not kind a triangle.

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