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

It is currently 18 Oct 2019, 17:17

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The area of an equilateral triangle is √3 times that of a square. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
G
Joined: 07 Jun 2017
Posts: 161
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 16 Oct 2017, 03:24
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (01:28) correct 28% (02:07) wrong based on 110 sessions

HideShow timer Statistics

The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.com

_________________
Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post
Intern
Intern
User avatar
B
Joined: 15 May 2017
Posts: 33
GMAT 1: 770 Q51 V45
Re: The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 16 Oct 2017, 04:33
1
The area of an equilateral triangle is 3√3 times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. 1/2

B. 1/√3

C. 1/√2

D. √3

E. 2

When dealing with theoretical geometry, first write out the requisite formulas, in this case Area Triangle = 1/2 base x height and Area Square = side^2. From the ratio in the problem it can be determined that √3 = 1/2 base x height and 1 = side^2. Therefore, a side of the square = 1, and 2√3 = base x height. Because the ratio of the base to the height in an equilateral triangle is always 2:√3, divide each side of that equation by √3 to find that the base of the triangle is 2 and that the ratio of the length of a base of the triangle is 2 times that of a side of the square. The correct answer is choice E.

Alternatively, using simple logic and drawing a figure it should be possible to determine that the side of the triangle must be larger for the triangle to have an area √3 times that of a square, so eliminate choices A, B, and C which indicate that the side of the triangle is less than the side of the square. The ratio of the sides and that of the areas also would logically not be the same, so eliminate choice D. Choice E is the only logical option, and can be determined in relatively short order without any calculation. Consider these types of shortcuts when facing theoretical geometry problems.
_________________
M.S. Journalism, Northwestern University '09
Director of Online Tutoring, MyGuru
http://www.myguruedge.com


Find out more about online GMAT tutoring with MyGuru
http://www.myguruedge.com/gmat-prep/online-gmat-tutoring
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3554
The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 16 Oct 2017, 11:47
1
nkmungila wrote:
The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.com

If you know the formula for area of an equilateral triangle, the answer turns on translation and algebra.*

Area of an equilateral triangle, \(a\) = side:

\(\frac{a^2\sqrt{3}}{4}\)

"The area of an equilateral triangle [with side \(a\)] is \(\sqrt{3}\) times that of a square," with side \(s\). Translate:

(Area of square)(\(\sqrt{3}\)) = Area of triangle

\(s^2\sqrt{3}\) = \(\frac{a^2\sqrt{3}}{4}\)

Factor out \(\sqrt{3}\)

\(s^2 = \frac{a^2}{4}\)

\(\sqrt{s^2} = \sqrt{\frac{a^2}{4}}\)

\(s = \frac{a}{2}\)

Ratio of a side of the triangle to a side of the square? Rearrange the expression immediately above.

\(\frac{a}{s} = \frac{2}{1} = 2\)

Answer E

*If you don't know the formula, although deriving it is painstaking, it is completely possible. You drop an altitude and find the area of two 30-60-90 right triangles, described here and here
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.


Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 17 Oct 2017, 11:44
nkmungila wrote:
The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.com


We can let t = the side of the triangle and s = the side of the square; thus:

(t^2)(√3)/4 = (s^2)√3

(t^2)(√3) = (s^2)(√3)(4)

t^2 = (s^2)(4)

t^2/s^2 = 4/1

t/s = 2/1

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Status: preparing for GMAT
Joined: 29 Nov 2017
Posts: 22
GPA: 3.55
WE: Military Officer (Military & Defense)
Re: The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 19 Jan 2018, 11:57
generis wrote:
nkmungila wrote:
The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.com

If you know the formula for area of an equilateral triangle, the answer turns on translation and algebra.*

Area of an equilateral triangle, \(a\) = side:

\(\frac{a^2\sqrt{3}}{4}\)

"The area of an equilateral triangle [with side \(a\)] is \(\sqrt{3}\) times that of a square," with side \(s\). Translate:

(Area of square)(\(\sqrt{3}\)) = Area of triangle

\(s^2\sqrt{3}\) = \(\frac{a^2\sqrt{3}}{4}\)

Factor out \(\sqrt{3}\)

\(s^2 = \frac{a^2}{4}\)

\(\sqrt{s^2} = \sqrt{\frac{a^2}{4}}\)

\(s = \frac{a}{2}\)

Ratio of a side of the triangle to a side of the square? Rearrange the expression immediately above.

\(\frac{a}{s} = \frac{2}{1} = 2\)

Answer E

*If you don't know the formula, although deriving it is painstaking, it is completely possible. You drop an altitude and find the area of two 30-60-90 right triangles, described here and here



similar practice problems to this question?

Thank you in advance!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 19 Jan 2018, 12:09
1
destinyawaits wrote:
generis wrote:
nkmungila wrote:
The area of an equilateral triangle is \(\sqrt{3}\) times that of a square. What is the ratio of a side of the triangle to a side of the
square?

A. \(\frac{1}{2}\)

B. \(\frac{1}{\sqrt{3}}\)

C. \(\frac{1}{\sqrt{2}}\)

D. \(\sqrt{3}\)

E. \(2\)

http://www.expertsglobal.com

If you know the formula for area of an equilateral triangle, the answer turns on translation and algebra.*

Area of an equilateral triangle, \(a\) = side:

\(\frac{a^2\sqrt{3}}{4}\)

"The area of an equilateral triangle [with side \(a\)] is \(\sqrt{3}\) times that of a square," with side \(s\). Translate:

(Area of square)(\(\sqrt{3}\)) = Area of triangle

\(s^2\sqrt{3}\) = \(\frac{a^2\sqrt{3}}{4}\)

Factor out \(\sqrt{3}\)

\(s^2 = \frac{a^2}{4}\)

\(\sqrt{s^2} = \sqrt{\frac{a^2}{4}}\)

\(s = \frac{a}{2}\)

Ratio of a side of the triangle to a side of the square? Rearrange the expression immediately above.

\(\frac{a}{s} = \frac{2}{1} = 2\)

Answer E

*If you don't know the formula, although deriving it is painstaking, it is completely possible. You drop an altitude and find the area of two 30-60-90 right triangles, described here and here



similar practice problems to this question?

Thank you in advance!


Similar questions:
https://gmatclub.com/forum/if-b-is-sele ... 92903.html
https://gmatclub.com/forum/a-square-and ... 50220.html
https://gmatclub.com/forum/what-is-the- ... 37086.html
https://gmatclub.com/forum/the-diagonal ... 25839.html
https://gmatclub.com/forum/if-the-diago ... 46129.html
https://gmatclub.com/forum/if-the-heigh ... 06080.html
https://gmatclub.com/forum/an-equilater ... 67319.html
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13262
Re: The area of an equilateral triangle is √3 times that of a square. What  [#permalink]

Show Tags

New post 16 Jul 2019, 05:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: The area of an equilateral triangle is √3 times that of a square. What   [#permalink] 16 Jul 2019, 05:02
Display posts from previous: Sort by

The area of an equilateral triangle is √3 times that of a square. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne