Calculating Momentum of Object R: A Physics Problem

[mirandab17]

Three objects travel. Object P (4 kg) travels downward at 8.3 m/s. Object Q (2 kg) travels to the east at 7.2 m/s. Another object (R) is traveling at them from the south east corner.

What is the magnitude of the momentum of object R so that the combined masses remain
stationary after they collide?

I figured out that you simply create a triangle of the momentums, finding that 36 is the magnitude of the momentum of object R as the right answer. However, I don't really get what I did completely. Is it because this triangle represents conservation of momentum? Isn't the object R coming from the south east a separate factor? As in, as the hypotenuse of the triangle, doesn't it represent final momentum...?

Little confused here.

 

[Nugatory]

Momentum is a vector, and the rules for adding and subtracting vectors will be helpful here. A vector pointing to the southeast can rewritten as the sum of a vector pointing to the south and another vector pointing to the east.