question_answer

In \[\Delta \text{ABC}\], D is a point on AB and E is a point on BC such that \[\text{DE}|\,\,|\text{AC}\] and area of \[\Delta DBE=\frac{1}{2}\] area of \[\Delta \text{ABC}\]. Find\[\frac{AD}{AB}\].

A)  \[\frac{1-\sqrt{2}}{2}\]

B)  \[\frac{\sqrt{2}-1}{\sqrt{2}}\]

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

D)  \[\frac{\sqrt{2}+1}{2}\]