Math problem of the day

If the perimeter of square A is twice the perimeter of square B, then the quotient of the area of square A divided by the area of square B is equal to:

Answers variants: A. 1   B. 2   C. 3   D. 4   E. 5

Correct answer: D. 4

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)
Area(A) / Area(B) = 4
So, the correct answer is (D): 4