Question: Comparing Areas

Comment on Comparing Areas

considering the first given information that angle bce = 30 we can easily find out that this is a 30-60-90 triangle
Also as AC is the diagonal of rectangle ABCD therefore triangle ABC becomes 45-45-90 triangle which eventually fixes the way this fig looks so we can not extend or contract this figure to find out if this statement is sufficient or not.
However comparing these two triangles, we can easily find out bases of both triangle CBE and ABC, and from that information, we can find out base of triangle ACE and then we can compare bases of both triangles CBE ans ACE to answer our given question.So according to me this statement is sufficient.
Please correct me if I am wrong somewhere.
gmat-admin's picture

There's an error when you say: "Also as AC is the diagonal of rectangle ABCD therefore triangle ABC becomes 45-45-90"
IF we were told that ABCD is a SQUARE, then ABC definitely be a 45-45-90 triangle. However, we're told that ABCD is a RECTANGLE, in which case, we can't conclude that ABC is a 45-45-90 triangle.

Thanks for your quick response.Its clear now.


I did not understand why statement 1 is not sufficient.

The angle ACB is not 45°? so, ACE would be 15°?

Please explain me why am I wronging?

gmat-admin's picture

Hi Pedro,

IF it were the case that ABCD is a SQUARE, then angle ACB would be 45°. However, we're not told that ABCD is a square.


Does this imply that diagonals of rectangles are not angle bisector where as squares' are?
gmat-admin's picture

That is correct.

Here's an image that definitively shows that the diagonal of a rectangle is not an angle bisector:


Hi Brent, in triangle BCE, since we can deduce 90 and given 30, therefore can we say that this is 30-60-90 triangle?
gmat-admin's picture

Are you referring to statement 1?
If so the answer is yes.
The given information, ABCD is a RECTANGLE, tells us that angle B is 90 degrees.
So, when statement 1 tells us angle BCE = 30 degrees, we can then conclude that angle BEC = 60 degrees

Thanks Brent for confirmation. Yeah my bad forgot to mention St1.

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