Illustrator :: Get Miter-joined Vertices On Unfilled Right Triangle With 3 Different-colored Sides?

I want to create a right-angled triangle (just the three sides, no fill) where each side is a different color (say red, blue, and green). For generality, let's assume it's a scalene (rather than isosceles) right triangle. I want the weight of each line to be about 3pt. (But I guess that's not a crucial number. Let's say I'd like the sides to be 20 or 30 pts thick, for the thrill of it.) I know how to draw the three lines of specified width, make them different colors, and arrange them into a triangle. My problem is how to make the vertices (corners) look miter-joined rather than have them overlapping each other, which obviously looks terrible and like something an infant drew in Microsoft Paint. ;-) If I join the 3 paths into a single shape, they all become the same color, so I'm thinking I have to keep it as 3 separate lines (paths). The only solution I can think of is: Instead of drawing three lines of 3pt weight, draw three extremely thin rectangle shapes (about 3pt wide), one of each color, and rotate/position them so that they form the sides of a right-angled triangle. Then go in and do some visual surgery at the vertices to make the vertices look miter-joined.