The dissection into 3 triangles fails if we start from a square (the green and blue triangles become equal)
How many triangles are then necessary ? Solution
Dissect a rectangle into rectangles similar to each others is not hard.
(here 2×4, 4×8 and 5×10 inside a 9×10 rectangle)
But if all rectangles, including the big one, have to be similar and unequal ? Solution
How many rectangles at least if all rectangles have integer dimensions ? Solution
A square into similar non equal rectangles ? Solution