Let's Investigate Triangles

Vincent and Tara are making triangles with strips from the class construction set.

They have strips of three different lengths: 4 holes, 7 holes and 11 holes.

There are plenty of strips of each length. 

Vincent makes a triangle with two strips that are length 7 and one strip that is length 4, like this: 

Tara makes a triangle with three strips that are each length 11, like this:

How many different triangles can you make using strips that are length 4, length 7 and/or length 11?
You can use the interactivity below to try out your ideas if you do not have a construction set.

Can you find three strips which cannot be made into a triangle when you use them together?
Why is it impossible to make a triangle from those three strips?