GE90-115B (the only engine you can have on a 777-200LR/300ER). I think the chord doesn't change from the root to the tip that much - it's more that the blades are "twisted" so you are looking at them more edge-on at the center. The wavy shape reminds me of modern helicopter rotor blades that have that swept, shovel shape at the end which I believe makes them quieter. So my guess is it has to do with the way the shock waves from each blade interact with each other, i.e. it makes them quieter.
I often wander up to the intake of one of these and marvel at their awesomeness.
They are very popular with flight crews for photo ops too.