What is the perimeter of the square BEDF? (1) The area of the shaded

In my opinion the correct answer is E.
you can apply "rubber-band" geometry to the question to evaluate each statement:
s1--> you can pull point A to the left/right direction shrinking the square BEDF diagonal while maintaining the same area of 100-->NS
s2--> no one said the shaded area is symmetric so the added angle gives no added value-->NS

s1+s2--> still can move point A wile keeping both the area at 100 and the angle at 30deg --> NS

Analyzing the question:
There is no constraint on where \(A\) can be, so keep in mind it can go as far as you'd like. Asking for the perimeter of the square is the same thing as asking for its area, length, or diagonal. If we know one of these, we can find the others.

Statement 1:
We can make a very small square while retaining the area of the shaded region to 100 by extending \(A\) very far away, or create a bigger square with area of 100 by making \(A\) a vertice.

Statement 2:
No information on the areas so insufficient.

Combined:
We can move \(A\) up and down a line that is 30 degrees with respect to line segment DE. This will retain the 30-degree angle while changing the dimensions of the square: small square + far \(A\) or big square + close \(A\). Insufficient.

Ans: E

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