We write the first condition of the problem by the expression for the perimeter:
2 x A + 2 x B = 48.
We write the second condition of the problem as follows:
A + 2 x B = 36.
The result is a system of equations. The easiest way to solve it is by subtracting the second from the first equation. We get immediately A:
A = 12 (cm).
Now from the second equation we express B:
B = (36 – A) / 2;
B = 24/2;
B = 12 (cm).
Answer: the given rectangle is a square, where A = B = 12 cm.
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