We have been given the following potential side lengths.
8 m 10 m 19 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:& 8+10? > 19 ⇒ 18 ≯ 19
II:& 10+ 19? > 8 ⇒ 29 > 8
III:& 19+ 8? >10 ⇒ 27 > 10
Since Inequality I is not true, a triangle cannot have these sides.
