Rg4, b5; Qe5, Qh6: h5, Qc1+; Kh2, Qc2+; kh3, Qd3+; Rxd3; e4xd3; h6, Kh7; Rxg7, Kh8,; Rxg8, kxg8, Qg7+ mate

1) h4, a5

is it possible with h4

Vipinzamvar, why does one need to take pawns if one can checkmate?

what about:
1) R x g7, R xg7
2) Rd8+, Qg8
3) R x g8, K xg8
4) And then the white Queen can mop up the pawns.

I have only found mate in 11.

1.Rg4 a5
2.Rxc7 e3
3.Rh4 e2
4.Rxh7+ Kxh7
5.Qh4+ Kg6
6.Rxc6+ Kf5
7.Rf6+ Ke5
8.Qf4+ Kd5
9.Rd6+ Kc5
10.Qd4+ Kb5
11.Rxb6#