Let b be the side length of square B. Then the area of square B is
Area(B) = b*b = b²
and perimeter of square B is
P(B) = b+b+b+b = 4b
Since the perimeter of A is double this, it is
P(A) = 2*P(B) = 2*4b = 8b
Therefore the side length, which we may call a, of square A, is
a = P(A)/4 = 8b/4 = 2b
Hence the area of square A is
Area(A) = a*a = a²
Area(A) = (2b)²
Area(A) = 4b²
Area(A) = 4*Area(B)
and
Area(A) / Area(B) = 4
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So, the correct answer is (D): 4