Last visit was: 17 Jun 2024, 18:17 It is currently 17 Jun 2024, 18:17

Close

GRE Prep 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 GRE 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
Verbal Expert
Joined: 18 Apr 2015
Posts: 28946
Own Kudos [?]: 33720 [1]
Given Kudos: 25365
Send PM
avatar
Intern
Intern
Joined: 01 Sep 2017
Posts: 20
Own Kudos [?]: 31 [0]
Given Kudos: 0
Send PM
Intern
Intern
Joined: 19 Sep 2019
Posts: 48
Own Kudos [?]: 42 [0]
Given Kudos: 11
Send PM
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 11808 [0]
Given Kudos: 136
Send PM
Re: In the figure above, the circumference of the circle is 20π [#permalink]
3152gs wrote:
simon1994 wrote:
So the rectangle is going have the greatest Area if it is a square.

We know that the circle has a diameter of 20.

The square will have this diameter as its diagonal. In every sqaure the diagonal is a side * sqRoot of 2. So here it is 20/(sqRoot2).

If we multiply 20/(sqRoot2) we obtain 200.


Can you please elaborate why it has to be a square to have maximum area ?


Great question.
To prove that the maximum area occurs when the shape is a square, we'd need to use some calculus (which is beyond the scope of the GRE).
So, let's just say it's a general property.

Cheers,
Brent
Manager
Manager
Joined: 19 Feb 2021
Posts: 184
Own Kudos [?]: 175 [1]
Given Kudos: 425
GRE 1: Q170 V170
Send PM
Re: In the figure above, the circumference of the circle is 20π [#permalink]
1
What are the possibilities for the inscribed rectangle?
The inscribed rectangle can be stretched and pulled to extremes: extremely
long and thin, extremely tall and narrow, and somewhere in between:
The “long and thin” and “tall and narrow” rectangles have a very small area,
and the “in between” rectangle has the largest possible area. In fact, the
largest possible rectangle inscribed inside a circle is a square
In this problem, the circumference is equal to 20π = 2πr. Thus r = 10. The
square then has a side length of 10\sqrt{2}and an area of (10\sqrt{2} )2 = 200.
Prep Club for GRE Bot
[#permalink]
Moderators:
Moderator
1088 posts
GRE Instructor
218 posts

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