Isosceles Triangles

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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Problem

Isosceles Triangles printable sheet

Image
Isosceles Triangles


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?



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