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$\text{ABCD}$ is a rectangle. The points $\text{P}$ and $\text{Q}$ lie on $\text{AD}$ and $\text{AB}$ respectively. If the triangle $\text{PAQ, QBC}$ and $\text{PCD}$ all have the same areas and $\text{BQ} = 2$, then $\text{AQ} =$

1. $1+\sqrt{5}$
2. $1-\sqrt{5}$
3. $\sqrt{7}$
4. $2\sqrt{7}$

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