Calculate buffer distance by known area I have a rectangle with a known area S1 and known sides A and B, I need to make new rectangle around the first with area S2 by applying buffer operation to the first rectangle. How can I calculate buffer distance (D) to solve this problem?
 A: I am unfamiliar with what you mean by buffer distance, so I'm going to start by showing a general approach, then narrow things down by assuming you want a square "buffer" between each pair of corresponding vertices.
Let's say the two concentric rectangles are situated symmetrically. Let the width of the inner rectangle be $A$ and its length be $B$. For symmetry, the inner rectangle has to be centered both vertically and horizontally within the new larger rectangle. See image. 
So the corresponding dimensions of the outer rectangle will be $A + 2x$ and $B+2y$. You want the product to be $S_2$.
To achieve a square "buffer" between each of the vertices (corners), you can let $x=y$, so you can now write the equation:
$(A+2x)(B+2x) = S_2$
$AB + 4x^2 + 2x(A+B) = S_2$
And since $AB = S_1$,
$4x^2 + 2(A+B)x + (S_1 - S_2) = 0$
You can solve this using the quadratic formula (discarding the negative root) to give:
$$x = \frac{-2(A+B) + \sqrt{4(A+B)^2 + 16(S_2 - S_1)}}{8} = \frac{ \sqrt{(A+B)^2 + 4(S_2 - S_1)} - (A+B)}{4}$$
and here the $x$ should represent the buffer distance you refer to.
