In a triangle ABC, DE is a line segment which intersects AB at D and AC at E such that DE is parallel to BC. The line segment divides the triangle in two parts of equal area. What is \(\rm \frac{BD}{AB}\) equal to ?
1
\(\frac{\sqrt2-1}{2}\)
2
\(\frac{\sqrt2-1}{\sqrt2}\)
3
\(\frac{\sqrt3-1}{\sqrt3}\)
4
√2