We have been given the following potential side lengths.
6 4 11
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+XZ>YZ
XZ+YZ>XY
YZ+XY>XZ
Applying this theorem to the given side lengths, we have three inequalities.
I:6+4? >11 & ⇒ 10 ≯ 11
II:4+11? >6 & ⇒ 15 > 6
III:11+6? >4 & ⇒ 17 > 4
Since Inequality I is not true, a triangle cannot have these sides.
