Perimeter puzzle

If four copies of this triangle are joined together to form a parallelogram, what is the largest possible perimeter of the parallelogram?
Age
11 to 14
Challenge level
filled star filled star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Perimeter Puzzle
If you join four copies of the triangle shown, without gaps or overlaps, how many different parallelograms can you make? 

What are the perimeters of the different parallelograms?

This problem has been adapted from the UKMT Mathematical Challenges.