When extending the sides $AB,BC,CA$ of $\Delta ABC$ to $B',C',A'$ respectively, such that $AB' = 2AB$ , $CC' = 2BC$ , $AA' = 3CA$ .

geometry triangles problem-solving congruences-geometry

Chop it like so:

enter image description here

The purple triangles and pink triangles have the same area as the one in the centre. The green and brown(?) ones double, and the blue one triple.

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