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