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 350,000 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:

Re: PS: Area of Rectangle [#permalink]
03 Aug 2012, 06:17

7

This post received KUDOS

Expert's post

voodoochild wrote:

walker wrote:

Area of a rectangle ranges from 0 to area of square=2. S0, I and II is possible.

Bunuel / Walker, I have a question. If the diameter = 2 => diagonal of square =2 => 2(side of a square)^2 = 2 => (side of a square)^2 = 1.

Hence, the area of square is 1!

Thoughts?

If the length of a diagonal of a square is 2, then \(side^2+side^2= diagonal^2\) --> \(2*side^2=2^2\) --> \(side^2=area=2\).

You could get the side in another way: since the angle between a diagonal and a side in a square is 45 degrees, then \(side=\frac{diagonal}{\sqrt{2}}\) (from the properties of 45-45-90 triangle).

You could also get the area directly: \(area_{square}=\frac{diagonal^2}{2}=2\).

Complete solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01 II. 2.00 III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

Attachment:

m24-05.png [ 10.63 KiB | Viewed 3826 times ]

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the are of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0<area\leq{2}\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi{r^2}=\pi\approx{3.14}\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

Re: PS: Area of Rectangle [#permalink]
03 Aug 2012, 07:06

Bunuel wrote:

voodoochild wrote:

walker wrote:

Area of a rectangle ranges from 0 to area of square=2. S0, I and II is possible.

Bunuel / Walker, I have a question. If the diameter = 2 => diagonal of square =2 => 2(side of a square)^2 = 2 => (side of a square)^2 = 1.

Hence, the area of square is 1!

Thoughts?

If the length of a diagonal of a square is 2, then \(side^2+side^2= diagonal^2\) --> \(2*side^2=2^2\) --> \(side^2=area=2\).

You could get the side in another way: since the angle between a diagonal and a side in a square is 45 degrees, then \(side=\frac{diagonal}{\sqrt{2}}\) (from the properties of 45-45-90 triangle).

You could also get the area directly: \(area_{square}=\frac{diagonal^2}{2}=2\).

Complete solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

I. 0.01 II. 2.00 III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Look at the diagram below:

If the width of blue rectangle is small enough then its area could be 0.01.

Generally, the are of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle).

Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0<area\leq{2}\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi{r^2}=\pi\approx{3.14}\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible)

Answer: D.

The link to the figure is not working/missing...

Did you mean something like this? (See the attached figure)

We can make the area of the inscribed rectangle as close as possible to 0, when for example the length is getting closer, and closer to the diameter, while the width is getting closer and closer to 0.

The maximum area can be obtained when the height of the right triangle, which is half of the rectangle and it is inscribed in the half circle, is equal to the radius of the circle. In this case, the rectangle becomes a square.

Attachments

MAxRectangleAreaInCircle.jpg [ 24.29 KiB | Viewed 3822 times ]

_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: A rectangle is inscribed in a circle of diameter 2. Which of [#permalink]
28 Nov 2013, 17:46

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. _________________

Re: A rectangle is inscribed in a circle of diameter 2. Which of [#permalink]
12 Dec 2013, 11:45

A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle?

If the circle has a diameter of 2, then it's radius is 1 so it's area is pi*1^2 or simply pi. Pi is equal to 3.1415. A a rectangle of .01 or 2.0 could fit inside this circle but not a rectangle with an area larger than the circle.

D

I. 0.01 II. 2.00 III. 3.20

A. I only B. II only C. III only D. I and II only E. II and III only

Re: A rectangle is inscribed in a circle of diameter 2. Which of [#permalink]
21 Jul 2015, 05:59

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. _________________

On September 6, 2015, I started my MBA journey at London Business School. I took some pictures on my way from the airport to school, and uploaded them on...

When I was growing up, I read a story about a piccolo player. A master orchestra conductor came to town and he decided to practice with the largest orchestra...

Amy Cuddy, Harvard Business School professor, at TED Not all leadership looks the same; there is no prescribed formula for what makes a good leader. Rudi Gassner believed that...

We are thrilled to welcome the Class of 2017 to campus today, and data from the incoming class of students indicates that Kellogg’s community is about to reach a...