In the figure, θ_1+θ_2=(π)/2 and √ 3 (B E)=4(A B). If the area of C A B is 2 √ 3 -3 unit ^2, when (θ_2)/(θ_1) is the largest, then the perimeter (in…

In the figure, $\displaystyle \theta_1+\theta_2=\frac{\pi}{2}$ and $\displaystyle \sqrt{3}(B E)=4(A B)$. If the area of $\displaystyle \triangle C A B$ is $\displaystyle 2 \sqrt{3}-3$ unit $\displaystyle { }^2$, when $\displaystyle \frac{\theta_2}{\theta_1}$ is the largest, then the perimeter (in unit) of $\displaystyle \triangle C E D$ is equal to $\displaystyle \_\_\_\_$.