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

Question

TOUGH QUESTION https://gmatclub.com/forum/download/file.php?id=50750 What is the perimeter of the square BEDF? (1) The area of the shaded region is 100. (2) ∠ADE = 30 degrees. Untitled.png

chetan2u · Answer

You can simplify the question by visualizing the figure...

We require to know the value of a..
Both the statements give us information which is NOT sufficient to find a..

Now it is easy to imagine ABD as isosceles triangle and mark C, but we cannot say that from given information..

we can take the position of A as A' where the statement II is satisfied.
For statement I to be satisfied, We have to enlarge the figure as the area in A'BFD will go below 100. But by enlarging the value of a will become more.

Thus there is NO fixed value of a

E

nick1816 · Answer

Statement 1

Length of side of square= s
Length of AE= b

Area of shaded region=  (\frac{1}{2}*s^2)+\frac{1}{2}*(\sqrt{2}s+b)*\sqrt{2}s=100

We can't solve 2 variables with 1 equation.
Insufficient

Statement 2- Clearly insufficient

Combining 2 equations
Just by knowing angle ADE, we can't find a relationship between s and b

We also need either angle DAB or angle DAE to find the relation between s and b.

Insufficient

almogsr · Answer

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

TestPrepUnlimited · Answer

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

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

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