The long glue joint is probably doing most of your heavy lifting there, but a half lap would help keep the end seams together i think. Thats probably what i would do. I wouldnt scarf it unless you have lots of material or have trouble with neat half laps.
You should stagger the front and back end joints though (the ends of that 39 measurement). Where they line up, the middle board is going to take most of the load right there.