SOLUTION: How many different sized triangles can be formed using 2 cm,3cm,4cm,5cm and 6cm rods?

Question 885692: How many different sized triangles can be formed using 2 cm,3cm,4cm,5cm and 6cm rods?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE SOLUTION:
If we have only one rod of each length, triangles.

THE EXPLANATION:
Some sets of three rods would determine one triangle.
We can make such sets,
but some sets of rods would not make a triangle.
For example, the set of

rods, and the set of

do not make a triangle:

To make a triangle, the lengths of the two shorter rods must add up to more than the length of the longest rod.
The set

does make a triangle because 3cm + 4cm = 7cm > 5cm :

If we use the 2cm rod, the sets that do not form triangles are
{2cm,3cm,5cm} , {2cm,3cm,6cm} , and {2cm,4cm,6cm} ,
while {2cm,3cm,4cm} , {2cm,4cm,5cm} , and {2cm,6cm,6cm}
All the other sets (without the 2cm rod) form triangles:
{3cm,4cm,5cm} , {3cm,4cm,6cm} , {3cm,5cm,6cm} , and {4cm,5cm,6cm} .

NOTE:
With just one rod of each length we are forced to make scalene triangles (triangles with 3 different side lengths).
If we had 3 (or more) rods of each measure we could make more triangles.
We could make 5 equilateral and 12 isosceles triangles (if I am counting correctly).
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