We have been given the following potential side lengths.
3 in. 4 in. 8 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.
XY+YZ>XZ
YZ+XZ>XY
XZ+XY>YZ
Applying this theorem to the given side lengths, we have three inequalities.
I:3+4? >8& ⇒ 7 ≯ 8
II:4+8? >3&
III:8+3? >4&
Since the sum of one pair of side lengths is not greater than the third length, these side lengths will not form a triangle.
