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Uncanny Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Where is a good place to start?
Have you looked at some of the examples on the sheet?
How many different triangles do you think you can draw with the lengths of the two perpendicular and horizontal sides making any total up to $15$? Can you list some? How do you know you can list them all without missing any out?
Have you thought of trying the "family" of triangles with a height of one?
Do you need to draw all the triangles in a family to see if any meet the requirements? How can you tell?