Question

If two sides of a triangle measure $4cm$ and $6cm$ find all possible measurement (positive Integers) of the third side. How many distinct triangles can be obtained?

Answer 1

We know that the sum of two sides should be less than the third side.

So, let the length of the third side be $x$ cm.

$4+x>6=x>2$

$x<4+6=x<10$

Hence, $x=3,4,5,6,7,8,9$