This is easy once you figure it out (at least for me), but I liked solving it, so might as well post it.
Basically, let's say you have a square with side length 1, and you want to trisect into three regions with equal area using two diagonal lines. More specifically, these diagonal lines are are at a 45° angle to the sides of the square, and are perpendicular to each other, like shown in the picture above. One of these diagonal lines is in a corner of the square.
The question is: Where on the side of the square does the diagonal line touch it? it's more clearly shown with the diagram.
Answer below:
The answer is √(2/3), which can also be written as (√6)/3. The reason for this is pretty simple: A triangle's area is 1/2 times its base times its height. In this case, its base and height are the same unknown. We know the area, so we can write this as the equation 1/2 * x² = 1/3
1/2 * x² = 1/3
x² = 2/3
x = √(2/3)
