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'Isosceles Triangles' printed from http://nrich.maths.org/

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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 shows one example.

How many different triangles satisfy these conditions?


Try to draw them all. You may wish to use the interactivity below.

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


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Click here for a poster of this problem.