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"A and B are two rectangles with sides that have an integer value. The perimeter of A is two times the perimeter of B, and the area of B is two times the area of A. If one of the sides of A is 1, determinate all possible integer values of sides of the rectangles A and B".

I think this problem is easy but i can't figure it, the only thing that i determinate is if we evaluate the sides of A as x and 1 and the sides of B as y and z

We have a equation system like this:

$$ \left\{ \begin{array}{c} yz=2x \\ 2y+2z=x+1 \\ \end{array} \right. $$

Correct me if i'm wrong

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  • $\begingroup$ What makes you refer to this as a "big problem"? If it's you having trouble, I should warn you that users on this site don't really like that kind of title - you should try to state the actual problem, or at least the context it comes from, like "Finding integer solutions to a system of equations," instead. $\endgroup$
    – Chris
    Commented Jun 17, 2017 at 5:41
  • $\begingroup$ Your system seems to capture the conditions OK. Do you have any start on solving? $\endgroup$
    – coffeemath
    Commented Jun 17, 2017 at 6:00

1 Answer 1

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Substitute the first into the second, getting $$4y+4z=yz+2\\14=(y-4)(z-4)$$ and factor $14$

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