# Cutting a rectangle in pieces [closed]

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 ?

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