Question

Which of the following will create a triangle? Select all that apply. 20 in., 5 in., 18 in. O 5 ft 3 ft, 1 ft 45 cm, 18 cm, 20 cm 9 yd, 8 yd, 12 yd

Answer 1

Explanation:

The triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side:

For this problem we have to try these inequalities. If all of them are true, then you can create a triangle with those measures:

$\begin{gathered} 20+5>18\Rightarrow25>18\text{ true} \\ 20+18>5\Rightarrow38>5\text{ true} \\ 18+5>20\Rightarrow23>20\text{ true} \end{gathered}$

You can create a triangle with the first set of measures.

$\begin{gathered} 5+3>1\Rightarrow8>1\text{ true} \\ 5+1>3\Rightarrow6>3\text{ true} \\ 1+3>5\Rightarrow4>5\text{ false} \end{gathered}$

You cannot create a triangle with the second set of measures.

$\begin{gathered} 45+18>20\Rightarrow63>20\text{ true} \\ 45+20>18\Rightarrow65>18\text{ true} \\ 20+18>45\Rightarrow38>45\text{ false} \end{gathered}$

You cannot create a triangle with the third set of measures.

$\begin{gathered} 9+8>12\Rightarrow17>12\text{ true} \\ 9+12>8\Rightarrow21>8\text{ true} \\ 12+8>9\Rightarrow20>9\text{ true} \end{gathered}$

You can create a triangle with the fourth set of measures.

Answers:

• 20 in, 5 in, 18 in

,

• 9 yd, 8 yd, 12 yd