Question

The length of two sides of a triangle are $6$cm and $9$ cm. Write all the possible length of the third side.

Answer 1

According to triangle inequality, the third side s lies in the interval:
$s\in (|6-9|,6+9)⟹s\in (3,15)$
If $s$ has to be an integer, then all the possible lengths are:
$4\text{cm},5\text{cm},6\text{cm},7\text{cm},8\text{cm},9\text{cm},10\text{cm},11\text{cm},12\text{cm},13\text{cm},14\text{cm}$