We have been given the following potential side lengths.
6 m 14 m 10 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:6+14? >10& ⇒ 20 > 10
II:14+10? >6& ⇒ 24 > 6
III:10+6? >14& ⇒ 16 > 14
Since all three inequalities are true, a triangle can have these side lengths.
