Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2014, 19:54

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Rectangle PQST, with dimensions w*h, is inscribed in a circl

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
avatar
Joined: 06 Jul 2010
Posts: 75
Followers: 1

Kudos [?]: 35 [2] , given: 12

GMAT Tests User
Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 17 Aug 2010, 02:15
2
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (03:23) correct 40% (02:46) wrong based on 100 sessions
Attachment:
Untitled.png
Untitled.png [ 3.74 KiB | Viewed 748 times ]
Rectangle PQST, with dimensions w*h, is inscribed in a circle with a radius of 1. Triangle QRS is isosceles with QR = RS and is inscribed in the circle. If triangle QRS and rectangle PQST have the same area, then what is the length of h? (Note: Figure not drawn to scale.)

A. 1/4
B. 2/5
C. 1/3
D. 1/2
E. 2/3
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Dec 2013, 00:24, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
4 KUDOS received
Manager
Manager
avatar
Joined: 20 Jul 2010
Posts: 79
Followers: 5

Kudos [?]: 53 [4] , given: 32

Re: Geometry [#permalink] New post 17 Aug 2010, 03:22
4
This post received
KUDOS
The height of traingle QRS is (1 - (h/2)).

**Since the rectangle PQST shares the centre with Circle, h/2 falls in upper part and remaining h/2 falls in lower part.**

wh = (1/2) (w) (1 - (h/2)) --> h = 2/5

Cheers!
Ravi

---------------------------
Consider giving me some Kudos if you like it!!!
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [0], given: 6

GMAT Tests User
Re: Geometry [#permalink] New post 17 Aug 2010, 03:38
heyholetsgo wrote:
What is wrong about saying
wh=w/2(1-h)--> h=1/3


Can you explain how did you come with the equation ?

wh=w/2(1-h)--> h=1/3


Cheers
Manager
Manager
avatar
Joined: 06 Jul 2010
Posts: 75
Followers: 1

Kudos [?]: 35 [0], given: 12

GMAT Tests User
Re: Geometry [#permalink] New post 17 Aug 2010, 03:47
I don't get your equation.
My equations says that the area of the rectangle wh must equal the area of the triangle.
The height of the triangle is the radius minus the height of the rectangle-->(1-h)
Hence the area of the triangle is w*(1-h)
I don't see why we have to divide h by 2!

Thanks for help
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 70 [0], given: 6

GMAT Tests User
Re: Geometry [#permalink] New post 17 Aug 2010, 03:51
heyholetsgo wrote:
I don't get your equation.
My equations says that the area of the rectangle wh must equal the area of the triangle.
The height of the triangle is the radius minus the height of the rectangle-->(1-h)
Hence the area of the triangle is w*(1-h)
I don't see why we have to divide h by 2!

Thanks for help



Chuck it, I misread it and over looked the same area part and hence was confused that what's the relation between the rectangle and the triangle.

Thanks anyway..!

Cheers,
1 KUDOS received
Manager
Manager
avatar
Joined: 20 Jul 2010
Posts: 79
Followers: 5

Kudos [?]: 53 [1] , given: 32

Re: Geometry [#permalink] New post 17 Aug 2010, 04:00
1
This post received
KUDOS
Because, The rectangle & Circle share the same centre.
Manager
Manager
avatar
Joined: 06 Jul 2010
Posts: 75
Followers: 1

Kudos [?]: 35 [0], given: 12

GMAT Tests User
Re: Geometry [#permalink] New post 17 Aug 2010, 05:33
Damn, no I get. I always looked at it and thought the rectangle stands on the center!
THX!
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 1835
Followers: 167

Kudos [?]: 33 [0], given: 0

Premium Member
Re: Geometry [#permalink] New post 23 Dec 2013, 18:37
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 138 [0], given: 254

GMAT ToolKit User
Re: Geometry [#permalink] New post 02 Jan 2014, 05:38
nravi4 wrote:
The height of traingle QRS is (1 - (h/2)).

**Since the rectangle PQST shares the centre with Circle, h/2 falls in upper part and remaining h/2 falls in lower part.**

wh = (1/2) (w) (1 - (h/2)) --> h = 2/5

Cheers!
Ravi

---------------------------
Consider giving me some Kudos if you like it!!!


So why did they give us that the areas where the same?

Would love to hear some reactions

Cheers!
J :)
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18856
Followers: 3275

Kudos [?]: 22916 [1] , given: 2651

Re: Geometry [#permalink] New post 02 Jan 2014, 05:47
1
This post received
KUDOS
Expert's post
jlgdr wrote:
nravi4 wrote:
The height of traingle QRS is (1 - (h/2)).

**Since the rectangle PQST shares the centre with Circle, h/2 falls in upper part and remaining h/2 falls in lower part.**

wh = (1/2) (w) (1 - (h/2)) --> h = 2/5

Cheers!
Ravi

---------------------------
Consider giving me some Kudos if you like it!!!


So why did they give us that the areas where the same?

Would love to hear some reactions

Cheers!
J :)


The equation in red above equates the areas of the rectangle and the triangle.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 269
Location: India
Followers: 0

Kudos [?]: 51 [0], given: 29

Re: Geometry [#permalink] New post 28 Mar 2014, 05:51
Bunuel wrote:
jlgdr wrote:
nravi4 wrote:
The height of traingle QRS is (1 - (h/2)).

**Since the rectangle PQST shares the centre with Circle, h/2 falls in upper part and remaining h/2 falls in lower part.**

wh = (1/2) (w) (1 - (h/2)) --> h = 2/5

Cheers!
Ravi

---------------------------
Consider giving me some Kudos if you like it!!!


So why did they give us that the areas where the same?

Would love to hear some reactions

Cheers!
J :)


The equation in red above equates the areas of the rectangle and the triangle.



How do we get height of triangle=(1-h/2)?
Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 269
Location: India
Followers: 0

Kudos [?]: 51 [0], given: 29

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 28 Mar 2014, 05:55
In other words how do we know that the centre of the circle and the rectangle are the same?What am I missing here?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18856
Followers: 3275

Kudos [?]: 22916 [0], given: 2651

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 28 Mar 2014, 08:25
Expert's post
AKG1593 wrote:
In other words how do we know that the centre of the circle and the rectangle are the same?What am I missing here?


A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. A rectangle is the sum of two right triangles, thus the diagonals of a rectangle must lie on the diameter of the circle. Therefore the intersection of the diagonals must be the center of the circle.
Attachment:
Untitled.png
Untitled.png [ 4.13 KiB | Viewed 459 times ]


Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 269
Location: India
Followers: 0

Kudos [?]: 51 [0], given: 29

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 28 Mar 2014, 09:00
Bunuel wrote:
AKG1593 wrote:
In other words how do we know that the centre of the circle and the rectangle are the same?What am I missing here?


A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. A rectangle is the sum of two right triangles, thus the diagonals of a rectangle must lie on the diameter of the circle. Therefore the intersection of the diagonals must be the center of the circle.
Attachment:
Untitled.png


Hope it's clear.


Got it!
A very nice observation!Thanks,Bunuel!
Intern
Intern
avatar
Joined: 26 May 2012
Posts: 43
Followers: 0

Kudos [?]: 7 [0], given: 11

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 09 Apr 2014, 20:38
I am still confused at how we know the height of the triangle is 1-(h/2). Could someone please explain?
2 KUDOS received
Intern
Intern
avatar
Joined: 08 Apr 2014
Posts: 12
Followers: 1

Kudos [?]: 8 [2] , given: 3

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 09 Apr 2014, 23:19
2
This post received
KUDOS
Catalysis..letme try :)

As the triangle is a isosceles triangle, a perpendicular drawn from point R to QS will pass through the centre if extended further.
So, the the length of the line connecting R to centre is 1 (radius)
To get the height of triangle, we need to remove the height of the area covered by rectangle.
Given it is a rectangle, QS = PT (properties of rectangle)
Now QS can only be equal to PT if they are equidistant from the centre of circle (only equidistant chords can be equal)
So, in other words center lies in the middle of the rectangle and hence height from center to QS is h/2
Hence if we remove this from 1 (radius), we get the height of the triangle = 1 - h/2

*consider giving Kudos if you like the post
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 10

Kudos [?]: 138 [0], given: 254

GMAT ToolKit User
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink] New post 22 Apr 2014, 16:16
I think I got it. So given that QRS is an isosceles triangle we have that the diameter = 2, is equal to 2a + h

We also know that wh= aw/ 2

Therefore replacing we have that h=2/5

Answer is thus B

Or also:

Let's call the height of the isosceles triangle 'A'. So, we have wh = aw/2. 2h=a/. Now, we also know that 2h+h+2h=2 which is the diameter of the circle. Therefore, h=2/5. B is the correct answer

Hope this clarifies
Gimme some freaking Kudos if it helps

Cheers!
J :)
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl   [#permalink] 22 Apr 2014, 16:16
    Similar topics Author Replies Last post
Similar
Topics:
59 Experts publish their posts in the topic A rectangle is inscribed in a circle of radius r. If the alex1233 31 16 May 2012, 06:44
1 Experts publish their posts in the topic The interior of a circle is inscribed in a rectangle of side bmwhype2 14 03 Mar 2008, 13:27
2 greatest area of a rectangle inscribed in a circle mand-y 3 02 Jun 2006, 09:51
A rectangle is inscribed in a circle whose radius equals R. drdas 3 03 Oct 2004, 08:41
A rectangle is inscribed in a circle whose radius equals R. falcor 13 17 Sep 2004, 12:56
Display posts from previous: Sort by

Rectangle PQST, with dimensions w*h, is inscribed in a circl

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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

Powered by phpBB © phpBB Group and phpBB SEO

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®.