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]

Show Tags

17 Aug 2010, 03:15

4

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

58% (02:39) correct
42% (03:03) wrong based on 175 sessions

HideShow timer Statistics

Attachment:

Untitled.png [ 3.74 KiB | Viewed 2311 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.
_________________

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]

Show Tags

28 Mar 2014, 10:00

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]

Show Tags

10 Apr 2014, 00:19

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]

Show Tags

22 Apr 2014, 17:16

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

Re: Rectangle PQST, with dimensions w*h, is inscribed in a circl [#permalink]

Show Tags

08 Apr 2017, 01:06

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.
_________________

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

A lot has been written recently about the big five technology giants (Microsoft, Google, Amazon, Apple, and Facebook) that dominate the technology sector. There are fears about the...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...