We have been given the following potential side lengths.
5 cm 7 cm 10 cm
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:&5+7? >10 ⇒ 12 > 10
II:&7+10? >5 ⇒ 17 > 5
III:&10+5? >7 ⇒ 15 > 7
Since all three inequalities are true, a triangle can have these side lengths.
