We have been given the following potential side lengths.
5 6 9
We will check whether these sides can form a triangle. In order to do that, we will use the Triangle Inequality Theorem. This theorem tells us that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Applying this theorem to the given side lengths, we have three inequalities.
I: 5+6? > 9 ⇒ 11 > 9
II:6+ 9? > 5 ⇒ 15 > 5
III: 9+ 5? >6 ⇒ 14 > 6
Since all three inequalities are true, a triangle can have these side lengths.
