In the adjoining figure, XY is parallel to AC. If XY divides the triangle into two halves with equal area, compute AX/AB.
If the two areas are equal......then the area of the smaller triangle =1/2 area of larger triangle
Then......the scale factor of the smaller triangle to the larger = 1/ √2
This means that the height of the smaller triangle to the height of the larger = 1 / √2
Since both triangles are similar this also means that BX / AB =1 / √2
Therefore.....AX = AB - BX = √2 - 1
AX / AB = [ √2 - 1 ] / √2