Looks like equilateral triangles to me (60 degree triangles, each side the same length). There are specialty rulers that help cut the triangles, such as this one from Creative Grids:
https://www.amazon.com/gp/product/B0017RGKCC/
Measure the side of your quilt. Method 1: Probably the easiest way to figure out the finished size you need for the triangles is to cut a piece of freezer paper that length. Fold it in half, then in half again, and keep folding until you get to a reasonable size for the triangle base.
Be aware that the sides of the triangle will be different than the triangle's height. The above method helps determine the side of the triangle. The next method determines the height of the triangle (which will be the width of your border).
Method 2: Decide how wide you want the border to be, then use one of the specialty rulers to cut triangles that will finish at that width.
Use as many triangles as will fit inside your quilt top edge, and fill in the rest of the space with the background fabric. In other words, you would be floating the strip of colored triangles on each side of the border, filling in the corners and any excess space along the border edge with the background fabric. Without floating, it is unlikely you can get an exact number of triangles to fit your border without having to cut weird widths of fabric.
Here is a link to a video demo of the Creative Grids ruler (there are similar rulers by other manufacturers, used the same way):
https://video.search.yahoo.com/searc...0&action=click
You may want to heavily starch fabric before cutting the triangles. Only the base of each triangle will be on the straight-of-grain; the other two sides will be bias and will be sewn to similar bias sides of adjoining triangles. You want the straight-of-grain sides to be the raw edges of your border.