Bunuel wrote:
The circumference of a circle is \(10\pi\). Which of the following is not a possible value of the area of a rectangle inscribed in it?
A. 30
B. 40
C. \(20\sqrt{2}\)
D. \(30\sqrt{2}\)
E. \(40\sqrt{2}\)
Think about it - what is the constraint on a rectangle inside a fixed circle?
It can have very very little area (say the blue rectangle). Then we can start expanding it till it becomes the yellow rectangle (which is actually a square). If we try to expand it any more, its area will start decreasing again till it becomes very very small again (the green rectangle).
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Screenshot 2021-10-21 at 11.42.34.png [ 183.97 KiB | Viewed 432 times ]
Hence, there is no minimum area of the rectangle but there is a maximum possible area dependent on the value of the radius. So if 40 is an acceptable area of a rectangle, then 30 is certainly acceptable too. If 30*sqrt(2) is acceptable (which is about 42), then 40, 30 and 20*sqrt(2) are certainly acceptable too. Hence, the only value that would not be acceptable is the greatest value given i.e. 40*sqrt(2).
Answer (E)
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Karishma
Veritas Prep GMAT Instructor
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