Question

If two sides of a triangle measure $4\text{cm}$ and $6\text{cm}$ find all possible measurements (positive Integers) of the third side.

Answer 1

We know that the sum of two sides should be greater than the third side.
So, let the length of the third side be $x\text{cm}$.
$4+x>6=x>2$
and $4+6>x$
$\Rightarrow x<10$
Hence, $x=3,4,5,6,7,8,9$