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

It is currently 18 Jun 2019, 00:06

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

If the ratio between the diagonal of a square and the height of an equ

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55640
If the ratio between the diagonal of a square and the height of an equ  [#permalink]

Show Tags

New post 14 Sep 2018, 02:19
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

60% (02:53) correct 40% (03:10) wrong based on 22 sessions

HideShow timer Statistics

CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2940
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If the ratio between the diagonal of a square and the height of an equ  [#permalink]

Show Tags

New post 14 Sep 2018, 02:50
Bunuel wrote:
If the ratio between the diagonal of a square and the height of an equilateral triangle is 5/3, respectively, what is the ratio of their areas?


A. \(\frac{5\sqrt{3}}{6}\)

B. \(\frac{5\sqrt{3}}{18}\)

C. \(\frac{25\sqrt{3}}{9}\)

D. \(\frac{25\sqrt{3}}{18}\)

E. 25/18


ratio between the diagonal of a square and the height of an equilateral triangle is 5/3

\((s√2) / (√3a/2) = 5/3\)
Here, s is the side of square and a is the side of equilateral triangle

\(s/a = 5√3 / 6√2\)

Ratio of areas = \(s^2 / [(√3/4)*a^2] = (4/√3)*(5√3 / 6√2)^2 = (4*75)/(72√3) = 25/6√3 =\) \(\frac{25\sqrt{3}}{18}\)

Answer: option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Ask GMAT Experts Forum Moderator
User avatar
V
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1022
Location: India
GPA: 3.64
GMAT ToolKit User Reviews Badge CAT Tests
Re: If the ratio between the diagonal of a square and the height of an equ  [#permalink]

Show Tags

New post 14 Sep 2018, 03:10
1
Bunuel wrote:
If the ratio between the diagonal of a square and the height of an equilateral triangle is 5/3, respectively, what is the ratio of their areas?

A. \(\frac{5\sqrt{3}}{6}\)

B. \(\frac{5\sqrt{3}}{18}\)

C. \(\frac{25\sqrt{3}}{9}\)

D. \(\frac{25\sqrt{3}}{18}\)

E. 25/18


D/h = \(\frac{5}{3}\)
h = \(\sqrt{3}\) a /2 where a is the side of the triangle.
D/a = \(\frac{5}{2\sqrt{3}}\)
Area of square = D^2/2
Area of equilateral triangle = \(\sqrt{3} a^2/4\)
Ratio = \(2(\frac{D}{a})^2 / \sqrt{3}\) = \(\frac{25}{6{\sqrt{3}}}\) = \(\frac{25\sqrt{3}}{18}\)

Answer D.
_________________
Please give kudos, if you like my post

When the going gets tough, the tough gets going...
GMAT Club Bot
Re: If the ratio between the diagonal of a square and the height of an equ   [#permalink] 14 Sep 2018, 03:10
Display posts from previous: Sort by

If the ratio between the diagonal of a square and the height of an equ

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


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