Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths.

There are:

• yellow strips with $3$ holes
• black strips with $4$ holes,
• red strips with $5$ holes and
• green strips with $6$ holes.

There are plenty of strips of each colour. 

Vincent makes a triangle with a green strip, a yellow strip and a red strip.

Tara makes a triangle with two green strips and one red strip and another triangle with three black strips.

How many different triangles can you make with these lengths?

Can you find three strips which cannot be made into a triangle when you use them together?