Question 68
Let $\triangle ABC$ be a triangle such that $\angle A = 90^\circ$. Determine whether it is possible to partition $\triangle ABC$ into 2006 smaller triangles in such a way that
$1^\circ$ Each triangle in the partition is similar to $\triangle ABC$;
$2^\circ$ No two triangles in the partition have the same area.
Explain your answer!
$1^\circ$ Each triangle in the partition is similar to $\triangle ABC$;
$2^\circ$ No two triangles in the partition have the same area.
Explain your answer!