In this case, the statement in A is correct, but the statement in B is not. This is because A only involved addition while B involves multiplication.
To see that this is correct, just do a simple example. Imagine one rectangle whose sides are 2 and 4 units and another whose sides are 4 and 8. The second is two times the first, right.
So now look at the perimeters. They will be 12 and 24 units, respectively. So the second is still two times the first.
But the second rectangle's area is four times the first (2*4 as opposed to 4*8).