Fine if any maths bod wants to have a go:
I have a right angled triangle. I want to split it into a trapezium and a smaller triangle, such that the trapezium has the area of 7/16 of the intial triangle. I want to make a cut perpendicular to one of the edges perpendicular to one of the edges adjacent to the right angle (not the hypotenuse). How far along does the edge does the cut have to be? Prove that it applies to any right angled triangle. No calculus needed.