Question

Determine if the following side lengths could form a triangle. Prove your answer with an inequality 52,37,42

Answer 1

Recall that in order to a, b, and c be the lengths of the sides of a triangle they must satisfy the following inequalities:

`\begin{gathered} a+b>c, \\ a+c>b, \\ b+c>a\text{.} \end{gathered}`

Answer:

Notice that:

`\begin{gathered} 52+37=89>42, \\ 52+42>37, \\ 37+42=79>52. \end{gathered}`

Therefore 52, 37, and 42 can be the lengths of the sides of a triangle.