Question

A triangle has two sides of lengths 6 and 9. What value could the length of the third side be?

Answer 1

The sum of the lengths of two sides of a triangle must always be less than or equal to the third side. So, if we let the third side be x, we have:

$\begin{cases}6+x\geq9\\x+9\geq6\\6+9\geq x\end{cases} \iff \begin{cases}x\geq3\\x\geq -3\\x\leq 15\end{cases} \iff \begin{cases}x\geq3\\x\leq 15\end{cases}$