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Isosceles Triangles

Age 11 to 14
Challenge Level

This question is about isosceles triangles with an area of 9 cm$^2$.

One of the vertices must be at the point (20, 20).
Each vertex of the triangle must be at a grid point of a square grid,
so all the vertices will have whole number coordinates.
How many different triangles satisfy these four conditions?

Try to find them all. You may wish to use the GeoGebra applet below.

Can you explain how you know that you have found them all?

Click here for a poster of this problem.