We have been given the following potential side lengths.
4 m 5 m 9 m
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:& 4+5? > 9 ⇒ 9 ≯ 9
II:& 5+ 9? > 4 ⇒ 14 > 4
III:& 9+ 4? >5 ⇒ 13 > 5
Since Inequality I is not true, a triangle cannot have these sides.
