Question

Determine if the side lengths could form a triangle. Use an inequality to justify your answer.12 cm, 25 cm, 12 cm

Answer 1

The triangle inequality theorem states that the sum of any 2 sides of the triangle must be greater than the third one.

For example if we have the triangle ABC, with sides AB, BC and CA, the theorem applies if

`\begin{gathered} AB+BC>CA \\ AB+\text{CA}>BC \\ BC+CA>AB \end{gathered}`

So for the given side lengths 12cm, 25cm and 12 cm

`\begin{gathered} 12+25>12 \\ 37>12 \end{gathered}`

For these sides it checks out

`\begin{gathered} 12+12>25 \\ 24>25 \end{gathered}`

For these sides it does not check

`\begin{gathered} 25+12>12 \\ 37>12 \end{gathered}`

For these sides it checks out

Since the sum of the sides with length 12cm isn't greater than the third side, with measure 25 cm, then we can concluce that these three side lengths cannot form a triangle.