Question

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

Answer 1

All possible measurement for the third side are $3$ cm, $4$ cm, $5$ cm, $6$ cm, $7$ cm, $8$ cm and $9$ cm.

Total $7$ triangles can be obtained.

sum of two sides is always greater than $3^{rd}$ side.

$a=4$

$b=6$

$c=$ numbers we let

$a+b>c$

$b+c>a$

$c+a>b$