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Isosceles Triangles

Age 11 to 14 Challenge Level:

Isosceles triangles have two equal sides.

The area of a triangle is half the base times the height.

Any of the three vertices of the triangle can be at $(20, 20)$.

There are sets of identical (congruent) triangles with an area of $9$cm$^2$.
How many triangles are there in each set? How many sets?