Rectangle Triangle dissection Problem

The problem is, given a rectangle, to cut off three triangles from the corners of the rectangle so that all three triangles have the same area. Or, expressed another way, to find a triangle inside a given rectangle (any rectangle) which when it is removed from the rectangle leaves three triangles of the same area. As shown here, the area of the leftmost triangle is x(w+z)/2. The area of the top-right triangle is yw/2. The area of the bottom triangle is (x+y)z/2. Making these equal means:

x(w+z) = yw and x(w+z)= z(x+y). The first equation tells us that x = yw/(w+z).

The second equation, when we multiply out the brackets and cancel the zx terms on each side, tells us that xw=zy. This means that y/x=w/z.

Putting this in other words, we have our first deduction that

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