I saw a problem on brilliant.org. It goes like this:

As usual I first turned to algebra! I found a solution though I felt it used too many 'tricks' for my liking. And I made several arithmetic errors which slowed me down. So I decided to see if there was another approach... perhaps a geometric or graphical one.

I opened Geogebra. I am not that proficient at using it and there are so many tools I haven't figured out yet but it allows me to play and experiment and it so often gives more insight into problems.

In this case I set a varying side length of the square and fixed the pink and green triangle areas. The right hand side shows the area of the yellow triangle plotted against the side length of the square. The solution occurs where the area of the yellow triangle is 3. In this diagram that is where the curve crosses the purple line which is at y = 3.

It gave me insight into why I could disregard some of my algebraic solutions and also threw up some more interesting questions. In particular, what is happening when the side length is between 2 and about 2.8? Why is there a little bump there? Curiouser and curiouser...

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