Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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: 

Image
Let's Investigate Triangles

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

Image
Let's Investigate Triangles

 

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?