Question

Determine if the side lengths could form a triangle, Use an inequality to prove your answer16 m, 21 m, 39m

Answer 1

No

Step-by-step explanation:

To determine if the side lengths could form a triangle, we use the triangle inequality.

By the triangle Inequality, If the sum of the lengths of any two sides is greater than the third side, then they can form a triangle.

Given the side lengths: 16m, 21m, 39m

`\begin{gathered} 16+21>39 \\ 37>39\text{ (False)} \end{gathered}`

Similarly:

`\begin{gathered} 16+39>21 \\ 55>21\text{ (True)} \end{gathered}`

Finally:

`\begin{gathered} 39+21>16 \\ 60>16\text{ (True)} \end{gathered}`

• We see that ,the sum of the two lengths (16 and 21) is not greater than the third side 39.

,

• Although the other two cases hold, the three cases must hold for it to form a triangle.

Thus, the side lengths cannot form a triangle.