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'Making Rectangles, Making Squares' printed from http://nrich.maths.org/
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Imagine you have any number of equilateral triangles all of the same size as well as a large number of $30$ $^\circ$ , $30$ $^\circ$ , $120$ $^\circ$ isosceles triangles with the shorter sides the same length as the equilateral triangles.
Using these triangles how many differently shaped rectangles can you build?
Can you make a square?
The interactivity below may help you with this problem. Click
on the green or yellow triangles to get a copy. Drag the triangle
by its interior to the required position and drag any vertex to
rotate it.
This text is usually replaced by the Flash movie.