Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1




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

Each vertex of the triangle must be at a grid point of a square grid
(all the vertices will have whole number coordinates).

One of the vertices must be at the point (20, 20).

The picture on the left shows one example.

How many different triangles satisfy these conditions?


Try to draw them all using the interactivity below.

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




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A poster of this problem is available here.




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Published February 2005,January 2007.