The area of square S is equal to the area of rectangle R. What is the

A smart approach in this question is to try and look for the area of the rectangle. Since the area of the rectangle is equal to the area of the square, we will able to find the length of the side of the square, and hence the perimeter of the square.

It’s clear, therefore, that statement II will be sufficient when taken alone. So, answer options A, C and E can be eliminated.

From statement I alone, if x is the side of the square, then the length of one of the sides of the rectangle will be 2x.

If l = 2x , then b = \(\frac{x}{2}\) so that area of rectangle = area of square = \(x^2\).
If b = 2x, then l = x/2. But this is not possible since the length of a rectangle is conventionally greater than the width.

But, even in the first case, knowing that the area is \(x^2\) is not like knowing the value of x, from which the perimeter of the square can be found out.
Statement I alone is insufficient. The correct answer option is B.

Glancing through the statements and the data that they might possess, will prevent you from following a one-dimensional approach to DS questions. In this question, you saw that we started off by analyzing Statement II because it provided the data that we wanted. Because we did this, it also helped us understand that Statement I was insufficient.
Of course, I don’t want to convey the idea that this should become the norm; in exceptional questions like the above, you could probably break the rules.

Hope this helps!

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