Consider two similar triangles (same base to altitude ratio), one having a base of 15ft and another of 12ft. The altitude of a triangle having a base of 15ft is 60, and another of 12ft is unknown (let's say x). So, using ratio 12/x=15/60. Solving this will give x = 48.
Whenever we have a triangular shape load (uniformly varying load) the point of application of load will be L/3 from the bigger side (at the centroid of the triangle).
For uniformly varying load(UVL), the load will act at 1/3 of the total length of UVL from the larger side. 12 x 1/3 = 4 ft, larger side is B, hence 4ft from point B.
I think you are talking about the load obtained by the externally applied uniformly varying load? If yes. The following discussions may clear your doubts. The value of 576 will be obtained if we had a uniformly distributed load UDL (12*48=576) but in this case, we have a uniformly varying load (UVL), hence (1/2*12*48=288). It is the same like the area of a rectangle (UDL) is b*h but the area of a triangle (UVL) is 1/2*b*h.
