Question

Give two-sided of a triangle, find a range of a possible side length of the third side 24 and 52

Answer 1

For a triangle to be possible with 3 given lengths, the largest side must be lower than the sum of the two remaining sides.

Let L be the length of the third side. There are two cases:

If L is the largest side, then:

`\begin{gathered} L<24+52 \\ \Rightarrow L<76 \end{gathered}`

If L is not the largest side, then the largest side has a measure of 52 and: