We have been given the following potential side lengths.
3 4 8
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: 3+4? > 8 ⇒ 7 ≯ 8
II:4+ 8? > 3 ⇒ 12 > 3
III: 8+ 3? >4 ⇒ 11 > 4
Since Inequality I is not true, a triangle cannot have these sides.
