We have been given the following potential side lengths.
2 12 m 1 34 m 5 18 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.
XY+YZ>XZ
YZ+XZ>XY
XZ+XY>YZ
Applying this theorem to the given side lengths, we have three inequalities.
I:&2 12+1 34? >5 18& ⇒ 4 14 ≯ 5 18
II:&1 34+5 18? >2 12&
III:&5 18+2 12? >1 34&
Since the sum of one pair of side lengths is not greater than the third length, these side lengths will not form a triangle.
