The ancient Greeks, being masters of geometric manipulation, often tried their hand at "squaring" various shapes. This involved using only the most fundamental rules of geometry to construct a square whose area equals the area of the original shape.
Can you follow in their footsteps and square a simple triangle?
The solution must hold for all types of triangles.
(In reply to re: Solution
Another way of getting it is realizing that triangles APC and CAQ are similar, and thus PA/AC=AC/AQ, or AC²=PA.AQ, as desired.
As a matter of fact, I solved it this way; I didn't know your way of solving it, which is new to me!