4. Given that the side lengths of rectangle $A$ are $a$ and $b$. If there is always another rectangle $B$ such that the ratio of the perimeter of rectangle $B$ to the perimeter of rectangle $A$ and the ratio of the area of rectangle $B$ to the area of rectangle $A$ are both equal to $k$. Then the minimum value of $k$ is
4. $\frac{4 a b}{(a+b)^{2}}$