We have been given the following potential side lengths.
2 yd 9 yd 10 yd
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:& 2+9? > 10 ⇒ 11 > 12
II:& 9+ 10? > 2 ⇒ 19 > 2
III:& 10+ 2? >9 ⇒ 12 > 9
Since all three inequalities are true, a triangle can have these side lengths.
