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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]
17 Aug 2010, 02:15
2
This post received KUDOS
2
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
65% (hard)
Question Stats:
62% (03:29) correct
38% (03:01) wrong based on 143 sessions
Attachment:
Untitled.png [ 3.74 KiB | Viewed 1323 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.)
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!
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 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. _________________
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]
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.
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]
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.
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]
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
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]
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
gmatclubot
Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl
[#permalink]
22 Apr 2014, 16:16
The “3 golden nuggets” of MBA admission process With ten years of experience helping prospective students with MBA admissions and career progression, I will be writing this blog through...
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...