question_answer

In \[\Delta \,ABC,\] PQ is a line segment intersecting AB at P and AC at Q such that \[PQ\parallel BC\] and PQ divides \[\Delta \,ABC\] into two parts equal in area, find \[\frac{BP}{AB}\].

A)  \[\frac{\sqrt{2-1}}{\sqrt{2}}\]                

B)  \[\frac{1+\sqrt{3}}{2}\]

C)  \[\frac{\sqrt{5+2}}{3}\]           

D)  \[\frac{1+\sqrt{2}}{\sqrt{3}}\]

E)  None of these