We have been given the following potential side lengths.
2.1 in. 4.2 in. 7.9 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:2.1+4.2? >7.9& ⇒ 6.3 ≯ 7.9
II:4.2+7.9? >2.1&
III:7.9+2.1? >4.2&
Since the sum of one pair of side lengths is not greater than the third length, these side lengths will not form a triangle.
