Let
$A_1=\left\{(x, y):|x| \leq y^2,|x|+2 y \leq 8\right\}$ and
$A_2=\{(x, y):|x|+|y| \leq k\}$.
If $27\left(\operatorname{Area} A_1\right)=5\left(\operatorname{Area} A_2\right)$, then $k$ is equal to :
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