GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2019, 11:06

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The number of inches in the perimeter of an equilateral triangle equal

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59725
The number of inches in the perimeter of an equilateral triangle equal  [#permalink]

### Show Tags

19 Mar 2019, 02:38
1
3
00:00

Difficulty:

45% (medium)

Question Stats:

75% (02:18) correct 25% (01:12) wrong based on 16 sessions

### HideShow timer Statistics

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) $$\sqrt{3}*\pi$$

_________________
Manager
Joined: 05 Oct 2017
Posts: 102
Location: India
Schools: ISB '21, IIMA , IIMB
GPA: 4
WE: Analyst (Energy and Utilities)
Re: The number of inches in the perimeter of an equilateral triangle equal  [#permalink]

### Show Tags

19 Mar 2019, 03:10
Bunuel wrote:
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) $$\sqrt{3}*\pi$$

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 =$$9/(\pi * \sqrt{3})$$
=$$3\sqrt{3}/\pi$$

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: The number of inches in the perimeter of an equilateral triangle equal  [#permalink]

### Show Tags

19 Mar 2019, 03:26
Bunuel wrote:
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) $$\sqrt{3}*\pi$$

As discussed here: https://www.veritasprep.com/blog/2013/0 ... relations/
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

_________________
Karishma
Veritas Prep GMAT Instructor

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The number of inches in the perimeter of an equilateral triangle equal  [#permalink]

### Show Tags

19 Mar 2019, 10:49
Bunuel wrote:
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) $$\sqrt{3}*\pi$$

Side of the triangle = sqrt(3) * Radius of the circle

so

given
3s=pi * r^2
r^2 = 3s/pi
s^2/3 = 3s/pi
so s= 9pi
or say
radius = 9pi/√3 = $$\frac{3\sqrt{3}}{\pi}$$
IMO B
Re: The number of inches in the perimeter of an equilateral triangle equal   [#permalink] 19 Mar 2019, 10:49
Display posts from previous: Sort by