The minimum case would be if you can place all these 4 input rectangles
in the vertical plane of the resultant recatangle, and along its
diagonal.

So suppose dimensions of 4 rectangles are
(x1,y1),(x2,y2),(x3,y3),(x4,y4) and of the resultant rectangle is
(x,y).

Then solution is all (x,y) that satisfy the condition

min(x1,y1,x2,y2,x3,y3,x4,y4) <= (x,y)^(1/2).

Thanks,
Satish


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