We have been given the following potential side lengths.
10 cm 12 cm 20 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.
Applying this theorem to the given side lengths, we have three inequalities.
I: 10+12? > 20 ⇒ 22 > 20
II:12+ 20? > 10 ⇒ 32 > 10
III: 20+ 10? >12 ⇒ 30 > 12
Since all three inequalities are true, it is possible for a triangle to have these side lengths.
