Yesterday evening, I was merrily meandering my way around Pinterest, as you do, when a triangle-based puzzle caught my eye. I was poised to peruse this further when “stuff” started to happen (wife, son, supper, two stupid cats… need I say more) and I never got around to seeing what it was all about. Tricky triangle puzzle (Click image to see a larger version — Image source: Max Maxfield)

The way I remember it is that there are four identical triangles mounted side-by-side. A line is drawn from the bottom left-hand corner of the left-hand triangle to the apex of the right-hand triangle as shown in my diagram.

Let’s start by assuming these are equilateral triangles, which means all three angles are the same (that is, beta == alpha). Is there a simple formula that we can use to define the ratio of the green and blue areas?

Next, assuming we can determine such a formula, does this hold true if our triangles are isosceles (that is, beta != alpha)? I await your response with dread antici…