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19 Mar 2019, 02:38
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
82% (02:12) correct
18%
(01:24)
wrong
based on 17
sessions
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The number of inches in the perimeter of an equilateral triangle equals the number of square inches in the area of its circumscribed circle. What is the radius, in inches, of the circle?
(A) \(\frac{3\sqrt{2}}{\pi}\)
(B) \(\frac{3\sqrt{3}}{\pi}\)
(C) \(\sqrt{3}\)
(D) \(\frac{6}{\pi}\)
(E) \(\sqrt{3}*\pi\)
(A) \(\frac{3\sqrt{2}}{\pi}\)
(B) \(\frac{3\sqrt{3}}{\pi}\)
(C) \(\sqrt{3}\)
(D) \(\frac{6}{\pi}\)
(E) \(\sqrt{3}*\pi\)
shuvodip04
Joined: 05 Oct 2017
Last visit: 03 Mar 2022
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Location: India
Concentration: Finance, International Business
Schools: IIMB IIMA ISB'22 (S) IIMA PGPX'22 (I)
GMAT 1: 660 Q48 V33
GMAT 2: 700 Q49 V35 (Online)
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19 Mar 2019, 03:10
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Bunuel
The question states that the numerical value of perimeter of the equilateral triangle is equal to the value of the area of the circumscribed circle.
Let side of the triangle be = x
Hence perimeter = 3x
Height of the triangle =\(\sqrt{3}x/2\)
In case of equilateral triangle the height and median are the same lines. And the centroid is also the circumcentre. Hence the centre of the circle will be same as centroid.
We know the median of the triangle is divided by the centroid in the ration 2:1.
So the radius of the circumcircle = \(2/3*\sqrt{3}x/2 = x/\sqrt{3}\)...i)
\(Area = \pi(x/\sqrt{3}) ^2\)
From question Area= Perimeter
\(\pi(x/\sqrt{3}) ^2 = 3x\)
\(=> x = 9/\pi\)
From ...i)
Radius of the circumcircle =\(9/(\pi * \sqrt{3})\)
=\(3\sqrt{3}/\pi\)
Answer (B)
Bunuel
If we have an equilateral triangle inscribed in a circle,
Side of the triangle = sqrt(3) * Radius of the circle
Given: Perimeter = 3*Side = Area of Circumscribed Circle = pi*Radius^2
3 * sqrt(3)*Radius = pi*Radius^2
Radius = 3*sqrt(3)/pi
Answer (B)
