Didn't we just do this somehwere else?

You need three things:

1) Conversion: Looking at the vertical labels in your not-to-scale drawing, one sees that 3W = 2L or W = (2/3)L. This makes the width of your figure L + (2/3)L = (5/3)L.

2) Reassurance: As luck would have it, in a textbook problem, we have 10L / [(5/3)L] = 6 AND 12L / 2L = 6. This means we CAN tile it without cutting anything. This also suggests how to orient the figure in the final construction.

3) Direction: 550 is WAY to many. Just adding the area of the pieces, 550*L*W = 550*L*(2/3)L = [366.66...]L^2 total area. Whereas, (10L)*(12L) = 120L^2. With 550, you can do the whole job THREE TIMES and have a little left over.