Math CentralQuandaries & Queries


Question from Palesa:

How many different types of triangles can be made with a perimeter of 12 matches?


The key fact that will help you get started is

Every side of a triangle must have a length which is larger than the sum of the lengths of the other to sides.

If this is confusing try to make a triangle with side lengths 4, 2 and 1 unit, or even one with sides of length 4, 3 and 1 unit.

Your units are matchstick lengths and the lengths of the sides must integers. (I expect you are not allowed to break the matchsticks). You have 12 matchsticks.

You can't have a side of length 12 matchsticks as there would be none left for the other two sides.

You can't have a side of length 11 matchsticks as that would leave you with only one other side.

You can't have a side of length 10 matchsticks since the other two sides would have length 1 and this violates the fact above.

Can the triangle have a side of length 9? What about 8?

Can you complete the problem now?


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