The importance of an active king in a pawns endgame!

This is a high accuracy bullet game (96% for me, 89% for my opponent). The endgame was a rook pawns endgame and my opponent chose to exchange the rooks. The game was drawable at that moment, but soon my opponent did a critical mistake so I managed to win easily the game as my king was more active. Remember that an active king is the most valuable piece in the endgames.