Combinations

Triangle ABC is enlarged by the green scale factor, and the result is enlarged by the yellow scale factor.

For A''B''C'' to be the same size as ABC, how should the scale factors be arranged?

Please enable Java for an interactive construction (with Cinderella).
a0 a1 a2 a3 a4
b0 b1 b2 b3 b4
c0 c1 c2 c3 c4
d0 d1 d2 d3 d4
e0 e1 e2 e3 e4
du er her f1 f2 f3 f4
g0 g1 g2 g3 g4
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