Question

Determine if the following side lengths could form a triangle. Prove your answer with an inequality 25,35,12

Answer 1

Given the following side lengths:

`25,35,12`

You need to apply the Triangle Inequality Theorem, in order to determine if they could form a triangle.

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides of the triangle is greater than the length of the third side of the triangle.

Therefore, using that theorem, you can set up the following inequalities:

`\begin{gathered} 25+35>12 \\ \\ 35+12>25 \\ \\ 25+12>35 \end{gathered}`

Solving each Addition on the left side of each inequality, you get:

`\begin{gathered} 60>12\text{ (True)} \\ \\ 47>25\text{ (True)} \\ \\ 37>35\text{ (True)} \end{gathered}`

As you can notice, the given sides satisfy the Triangle Inequality Theorem.

Therefore, the answer is:

- The side lengths could form a triangle.

- Proof:

`\begin{gathered} 25+35>12\text{ (True)} \\ 35+12>25\text{ (True)} \\ 25+12>35\text{ (True)} \end{gathered}`