We have been given the following potential side lengths.
1 15 km 4 12 km 3 34 km
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:&1 15+4 12? >3 34 ⇒ 5 710 > 3 34
II:&4 12+3 34? >1 15 ⇒ 8 14 > 1 15
III:&3 34+1 15? >4 12 ⇒ 4 1920 > 4 12
Since all three inequalities are true, a triangle can have these side lengths.
