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Similar Perimeter

Age 14 to 16 Short Challenge Level:

The lengths of the sides of a triangle A are 3, 4, and 6. 

Triangle B is similar to triangle A. One of the sides of triangle B has length 12.

What are the possible perimeters that triangle B could have?

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.