Let \(\Delta ABC\) be an equilateral triangle. How many squares in the same plane as \(\Delta ABC\) share two vertices with the triangle?


I know this was previously asked, but the answer given is wrong so I need help with this. Explain please?


I got 6 triangles because there's two for each side of the equilateral triangle but it's wrong.

 May 21, 2020

I can get nine --


Consider the vertices A and B; there are two squares that share the side AB (say ABXY with X and Y on one side of AB and X and Y on the other side of AB) and there is also the square that has A and B being opposite vertices of the square (square AXBY). 


So, that gives 3 squares using A and B; there will also be 3 squares using B and C and 3 squares using A and C.

 May 21, 2020

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