We have to cut a rectangle of size (MxN) into 3 pieces such that each pieces has a area a ,b and c respectively.How can we tell it's possible or not.

One condition is: M*N = a+b+c 

Is there any other condition ?


closed as off-topic by BmyGuest, Gamow, Fabich, CodeNewbie, Deusovi Jun 20 '16 at 14:38

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  • 4
    $\begingroup$ Cut it into three rectangles: M by a/M, M by b/M, and M by c/M. $\endgroup$ – f'' Jun 19 '16 at 14:52
  • $\begingroup$ no other conditions unless you require the divisions to be integer sized. $\endgroup$ – Jasen Jun 20 '16 at 7:03
  • 3
    $\begingroup$ Smells like somebody is trying to cheat in this online contest $\endgroup$ – Mohit Jain Jun 20 '16 at 9:13

Yes,you can do so as long as the areas work out. You can do two different patterns, shown below.enter image description here Either will always work. If the vertical dimension is $M$, the horizontals are $a/M, b/M, c/M$, which are guaranteed to add to $N$ by the area condition. On the right, the right rectangle is $M \times c/M$ (or any of the letters). Then the horizontal on the left is $N-c/M$ and the verticals are $\frac b{N-c/M}, \frac a{N-c/M}$


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