A rectangle is inscribed in a circle of radius r. If the rectangle is not a square, which of the following could be equal to the perimeter of the rectangle?
A. 2r(Sqrt 3)
B. 2r(Sqrt 3 + 1)
C. 4r(Sqrt 2)
D. 4r(Sqrt 3)
E. 4r(Sqrt3 + 1)
When shapes overlap, look for what they have IN COMMON.
When a rectangle is inscribed in a circle, the DIAGONAL of the rectangle is also the DIAMETER of the circle.
Almost every answer choice here includes √3.
√3 implies a 30-60-90 triangle.
The sides of a 30-60-90 triangle are in the following ratio:
1 - √3 - 2.
Let r=1, implying a diameter of 2.
Draw the following figure:
The perimeter of the rectangle above = 2 + 2√3. This is our target.
Now we plug r=1 into the answers to see whether one of them yields our target of 2 + 2√3.
Answer choice
B:
2r(√3 + 1) = 2(1)(√3 + 1) = 2√3 + 2.
Success!
The correct answer is
B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
