We have been given the following potential side lengths.
5 in. 8 in. 15 in.
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+8? > 15 ⇒ 13 ≯ 15
II:&8+ 15? > 5 ⇒ 23 > 5
III:& 15+ 5? >8 ⇒ 20 > 8
Since Inequality I is not true, a triangle cannot have these sides.
