It is currently 17 Dec 2017, 23:20

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The parallelogram shown has four sides of equal length. What is the

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

Hide Tags

Expert Post
5 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42670

Kudos [?]: 136007 [5], given: 12723

The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 20 Oct 2015, 23:19
5
This post received
KUDOS
Expert's post
40
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

63% (01:47) correct 37% (01:47) wrong based on 879 sessions

HideShow timer Statistics

Image
The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

(A) 1/2

(B) \(\frac{1}{\sqrt{2}}\)

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

(D) \(\frac{1}{\sqrt{3}}\)

(E) \(\frac{1}{2\sqrt{3}}\)

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-21_1114.png
2015-10-21_1114.png [ 3.11 KiB | Viewed 18950 times ]
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 136007 [5], given: 12723

5 KUDOS received
Intern
Intern
avatar
Joined: 30 Jan 2015
Posts: 2

Kudos [?]: 13 [5], given: 13

GMAT 1: 650 Q47 V33
The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 21 Oct 2015, 00:15
5
This post received
KUDOS
7
This post was
BOOKMARKED
IMO D.

The parallelogram has four equal sides (x), if the angles is 60° for one, the opposite angle is 60° and the other two are 120° each (360-60-60/2).

Therefore, the parallelogram diagonal bisects every angle to form four different 30-60-90 rectangle triangles (ratio: \(x : 2x : x\sqrt{3}\)).

Longer diagonal = \(2x\sqrt{3}\)
Shorter diagonal = \(2x\)

Therefore the ratio is \(\frac{2x}{2x\sqrt{3}}\) = \(\frac{1}{\sqrt{3}}\)

Kudos [?]: 13 [5], given: 13

1 KUDOS received
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1851

Kudos [?]: 1075 [1], given: 90

Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 21 Oct 2015, 00:29
1
This post received
KUDOS
Opposite angles of a parallegram are equal and sum of adjacent angles is 180 degree .
Each of the angles adjacent to 60 is 120 .
The shorter diagonal divies the parallelogram divides into 2 isosceles triangles .
Since all the sides of the parallelogram are equal , we get an equilateral triangle.
Therefore the shorter diagonal will be equal to length of sides of parallelogram = x

The longer diagonal divides parallelogram into 2 isoceles trianges with one angle 120 and the other 2 angles equal to 30 .

Since, the diagonals of a parallelogram are perpendicular bisectors ,the 2 diagonals divide the parallelogram into 4 - 30-60-90 triangles.

The sides of a 30-60- 90 triangle are in ratio 1:(3^(1/2)):2
Sin 60=(y/2)/x
Where y= length of the longer diagonal
=>(3^(1/2))/2=(y/2)/x
=>x/y=1/(3^(1/2))

Answer D
_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Kudos [?]: 1075 [1], given: 90

SC Moderator
User avatar
P
Joined: 13 Apr 2015
Posts: 1511

Kudos [?]: 1240 [0], given: 896

Location: India
Concentration: Strategy, General Management
WE: Information Technology (Consulting)
GMAT ToolKit User Premium Member CAT Tests
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 21 Oct 2015, 04:00
Let ABCD be our parallelogram with A = 60 degree and AB=BC=CD=AD=1
Opposite angles of a parallelogram are equal. So C = 60 degree.
Sum of adjacent angles = 180 degree. So B = 120 degree and D = 120 degree.
AC and BD be the diagonal.
Applying cosine rule (a^2 = b^2 + c^2 - 2bc(cos(included angle)),
AC^2 = 1 + 1 - 2cos(120) = 2 - 2(-0.5) = 3 --> AC = sqrt(3)
BD^2 = 1 + 1 - 2cos(60) = 2 - 2(0.5) = 1 --> BD = 1

Length of shorter diagonal to length of longer diagonal = 1:sqrt(3).

Ans: D

Kudos [?]: 1240 [0], given: 896

3 KUDOS received
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 888

Kudos [?]: 1930 [3], given: 302

Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 21 Oct 2015, 08:17
3
This post received
KUDOS
Bunuel wrote:
Image
The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

(A) 1/2

(B) \(\frac{1}{\sqrt{2}}\)

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

(D) \(\frac{1}{\sqrt{3}}\)

(E) \(\frac{1}{2\sqrt{3}}\)

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-21_1114.png


The figure must be a rhombus. Draw the diagonals on your scratch paper. You will now have two equiliteral triangles. The shorter diagonal is one side of such an equiliteral triangle. Let's say s=1.

To get the longer side of the diagonal of the rhombus, you have 2*height of the equiliteral triangle. If you split an equiliteral triangle into two parts, you will have two 30:60:90 triangles. The height of the equiliteral triangle if s = 1 is \(0.5*\sqrt{3}\) and the long diagonal will be \(2*0.5*\sqrt{3}\)

So you have \(1:\sqrt{3}\)

Answer D
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Kudos [?]: 1930 [3], given: 302

Retired Moderator
User avatar
P
Joined: 12 Aug 2015
Posts: 2226

Kudos [?]: 914 [0], given: 616

GRE 1: 323 Q169 V154
GMAT ToolKit User Premium Member
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 03 Apr 2016, 20:28
Here is what i did
Firstly the given ||gm has all sides equal => Rhombus

Now shorter diagonal is equal to the side of the ||gm as the equilateral triangle is formed.
Now to find the Longer diagonal i used the property that diagonals of rhombus bisect each other at a right angle..
so longer diagonal => √3 x side
hence the ratio => 1/3 or 1:3
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 914 [0], given: 616

SVP
SVP
User avatar
B
Joined: 06 Nov 2014
Posts: 1903

Kudos [?]: 552 [0], given: 23

Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 06 Jun 2016, 07:44
2
This post was
BOOKMARKED
Assume the length of each side = x

The other angles would be 60, 120 and 120.
Diagonal divides the parallelogram into half

Hence the shorter diagonal will make two equilateral triangles
Length of the shorter diagonal = length of side = x

For the longer diagonal.
The diagonal will divide the parallelogram in to isosceles triangles with angles 30, 120, 30
Dropping a perpendicular from top most point on to the diagonal, we have two triangles with angles 30, 60 and 90 with base as half the length of diagonal

Hypotenuse = x,
Cos 30 = base/x
base = (√3/2)*x

Hence the length of the diagonal = √3x

Ratio of the shorter to the longer diagonal = x : √3x = 1: √3

Correct Option: D

Kudos [?]: 552 [0], given: 23

9 KUDOS received
Manager
Manager
avatar
Joined: 21 Sep 2015
Posts: 82

Kudos [?]: 127 [9], given: 323

Location: India
GMAT 1: 730 Q48 V42
GMAT 2: 750 Q50 V41
Reviews Badge
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 08 Jun 2016, 03:31
9
This post received
KUDOS
3
This post was
BOOKMARKED
The parallelogram shown has four sides of equal length.

Inference : It is a rhombus.

Properties of Rhombus :

1) Diagonals are not congruent

2) Diagonals act as angle bisectors

3) Diagonals intersect at right angles and bisect each other

Hence we get a 30-60-90 triangle as shown below. Characteristic property of this triangle is that sides are in the ratio of 1:[ sqrt 3 ]:2

Shortest diagonal is the diagonal opposite the 30 degree angle and longest diagonal is the the one opposite 60 degree angle

Therefore ratio of shortest to longest is 1: sqrt 3
Attachments

Q139.png
Q139.png [ 6.59 KiB | Viewed 13512 times ]


_________________

Appreciate any KUDOS given ! :)

Kudos [?]: 127 [9], given: 323

1 KUDOS received
Intern
Intern
User avatar
Joined: 26 Nov 2015
Posts: 31

Kudos [?]: 19 [1], given: 5

Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 08 Jun 2016, 03:53
1
This post received
KUDOS
Lets assume that side = 1
now the shorter diagonal will belong to squeezed quadrilateral with one side = 1 - 1/2 = 1/2( being a 30-60-90 triangle on the right side) & one side = (3)^0.5/2
Longer diagonal will belong to enlarged quadrilateral with one side = 1 + 1/2 = 3/2 (being a 30-60-90 triangle but side will add) & one side = (3)^0.5/2

to find the diagonal we will apply Pythagoras to both rectangles
Squeezed Quadrilateral : ( 1/4 + 3/4) ^ 0.5 = 1
Enlarged Quadrilateral : ( 9/4 + 3/4 ) ^ 0.5 = 3^0.5

so the ratio= 1/ (3)^0.5
_________________

PS : I do mind kudos :)

Kudos [?]: 19 [1], given: 5

Intern
Intern
avatar
Joined: 13 Jun 2016
Posts: 19

Kudos [?]: 1 [0], given: 2

Premium Member
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 05 Oct 2016, 00:05
A novice question:

For parallelogram, i understand the rules of relationship for 30:60:90, opposite angels are congruent etc.

But how can we ascertain that when we split the parallelogram in to two parts , the 60 and 120 degrees angles on the vertices split in to exactly HALF? (i.e. 30 , 60 degrees)

Is that a math rule i've forgotten?

Please help thank you !

Kudos [?]: 1 [0], given: 2

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42670

Kudos [?]: 136007 [0], given: 12723

Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 05 Oct 2016, 01:09
xnthic wrote:
A novice question:

For parallelogram, i understand the rules of relationship for 30:60:90, opposite angels are congruent etc.

But how can we ascertain that when we split the parallelogram in to two parts , the 60 and 120 degrees angles on the vertices split in to exactly HALF? (i.e. 30 , 60 degrees)

Is that a math rule i've forgotten?

Please help thank you !


Usually diagonals of a parallelogram do not bisect the angles but here we have special kind of parallelogram - a rhombus, where the diagonals bisect the angles.

For more check here: math-polygons-87336.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 136007 [0], given: 12723

Manager
Manager
avatar
S
Joined: 03 Jan 2017
Posts: 196

Kudos [?]: 9 [0], given: 4

Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 25 Mar 2017, 09:17
the shorter diagonal is 1, because 60 can be calculated for the triangle->all sides are the same
the longer one is square root of 3, because if we split triangles we will get to ration x:2x:x*(3)^1/2, because this is triangle of 30:60:90 angles
2x is 1. hence our side is 2*1/2*3^1/2
Answer is E

Kudos [?]: 9 [0], given: 4

Top Contributor
Senior Manager
Senior Manager
User avatar
S
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 448

Kudos [?]: 527 [0], given: 59

Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 30 May 2017, 15:24
Top Contributor
Attached is a visual that should help.
Attachments

Screen Shot 2017-05-30 at 4.07.28 PM.png
Screen Shot 2017-05-30 at 4.07.28 PM.png [ 107.12 KiB | Viewed 6857 times ]


_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and online via Skype, since 2002.

GMAT Action Plan - McElroy Tutoring

Kudos [?]: 527 [0], given: 59

Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7799

Kudos [?]: 18155 [4], given: 236

Location: Pune, India
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 30 May 2017, 21:44
4
This post received
KUDOS
Expert's post
Bunuel wrote:
Image
The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

(A) 1/2

(B) \(\frac{1}{\sqrt{2}}\)

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

(D) \(\frac{1}{\sqrt{3}}\)

(E) \(\frac{1}{2\sqrt{3}}\)

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-21_1114.png


In a parallelogram, the opposite angles are equal. So angle opposite to 60 degrees is also 60.
Draw the shorter diagonal. Since the sides are equal, we see that we get two congruent equilateral triangles. The shorter diagonal is the side of each equilateral triangle and the longer diagonal is twice the altitude of each equilateral triangle.
We know that if the side of an equilateral triangle is s, its altitude is \(\sqrt{3}s/2\) and hence twice of its altitude is \(\sqrt{3}s\).

Required Ratio \(= s/\sqrt{3}s = 1/\sqrt{3}\)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18155 [4], given: 236

Intern
Intern
avatar
B
Joined: 01 May 2017
Posts: 9

Kudos [?]: 1 [0], given: 8

Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 16 Nov 2017, 18:57
A low level approach of assuming that each side is of length 1 and that we have two equilateral triangles joint together:
Attachments

tri.PNG
tri.PNG [ 27.74 KiB | Viewed 1821 times ]

Kudos [?]: 1 [0], given: 8

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1945

Kudos [?]: 1025 [1], given: 3

Location: United States (CA)
Re: The parallelogram shown has four sides of equal length. What is the [#permalink]

Show Tags

New post 20 Nov 2017, 11:38
1
This post received
KUDOS
Expert's post
Bunuel wrote:
Image
The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

(A) 1/2

(B) \(\frac{1}{\sqrt{2}}\)

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

(D) \(\frac{1}{\sqrt{3}}\)

(E) \(\frac{1}{2\sqrt{3}}\)

Kudos for a correct solution.

[Reveal] Spoiler:
Attachment:
2015-10-21_1114.png


We are given a parallelogram with equal sides, and we must determine the ratio of the length of the shorter diagonal to that of the longer diagonal. Since the sides are all equal, we know we have a rhombus, and the diagonals are perpendicular. Let’s sketch this diagram below.

Image

We should see that the diagonals bisect each angle of the rhombus, and thus we have created four 30-60-90 right triangles. Using our side ratio of a 30-60-90 right triangle, we have:

x : x√3 : 2x

Let’s use this side ratio to determine the lengths of each diagonal in terms of x.

Image

We can see that the length of the shorter diagonal is x + x = 2x, and the length of the longer diagonal is x√3 + x√3 = 2x√3. Thus, the ratio of the length of the shorter diagonal to the length of the longer diagonal is:

(2x)/(2x√3) = 1/√3

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1025 [1], given: 3

Re: The parallelogram shown has four sides of equal length. What is the   [#permalink] 20 Nov 2017, 11:38
Display posts from previous: Sort by

The parallelogram shown has four sides of equal length. What is the

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.