Copyright © University of Cambridge. All rights reserved.

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

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.