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

It is currently 23 Oct 2014, 23:35

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

In the xy-coordinate system, rectangle ABCD is inscribed

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5095
Location: Singapore
Followers: 19

Kudos [?]: 155 [0], given: 0

In the xy-coordinate system, rectangle ABCD is inscribed [#permalink] New post 23 Mar 2005, 23:37
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (01:03) correct 0% (00:00) wrong based on 0 sessions
In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x^2+y^2=25. Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y=3x+15 , what is the area of rectangle ABCD?

(A) 15
(B) 30
(C) 40
(D) 45
(E) 50
Senior Manager
Senior Manager
User avatar
Joined: 19 Nov 2004
Posts: 284
Location: Germany
Followers: 1

Kudos [?]: 10 [0], given: 0

 [#permalink] New post 24 Mar 2005, 01:44
30

Since the equation of the circle x^2+y^2=25, it represents a circle with centre at the origin and radius 5.

The explaination about the rectagle suggests that one of the diagonals is the diameter of the circle. Therefore, the two diametrically opposite points on the X axis would be (-5,0) and (5,0) the length of the diameter being 10.

Now, to find out about the location of point B. Since it lies on the circle, it should satisfy the equation x^2+y^2=25. Moreover, since it lies on the line y=3x+15, it should satisfy this equation as well. Solving these two equations, we get the possible values of B to be (-5, 0) and (-4, 3). Since B lies in the II quadrant, we take B to be (-4, 3).

Area of the rectangle ABCD = 2 * area of the triangle ABC
Area of triangle ABC = 1/2 * base * height = 1/2 * 10 * 3 = 15
=> Area of the rectangle = 2 * 15 = 30

Edit 1: calcuation mistake.
Edit 2: Attached a file displaying the problem pictorially.
Attachments

File comment: Figure for explaination
PS_Geometry.doc [25.5 KiB]
Downloaded 125 times

To download please login or register as a user

Intern
Intern
User avatar
Joined: 19 Jul 2004
Posts: 43
Followers: 1

Kudos [?]: 3 [0], given: 0

 [#permalink] New post 24 Mar 2005, 09:29
Agree the answer is 30.

The only thing required is the 'y' co-ordinate of (B), which can be easily found by substituting the value of 'x' from y = 3x + 15 ==> x = (y-15)/3

into equation of circle. It gives y = 3 and y = 0. Obviously y = 0 is the corordiante for 'C'.

Now diagonal is the base of the 'half-rectangle', whose height is '3' (we just found). This diagonal is the diameter of circle = 10

Hence area of triangle = 1/2 * 10 * 3

Hence area of rectangle = 2 * area of triangle = 30

Ketan
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5095
Location: Singapore
Followers: 19

Kudos [?]: 155 [0], given: 0

 [#permalink] New post 25 Mar 2005, 04:33
any other takers ??? :-D
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5095
Location: Singapore
Followers: 19

Kudos [?]: 155 [0], given: 0

 [#permalink] New post 27 Mar 2005, 01:29
both of you are right, the answer is 30. :-D
  [#permalink] 27 Mar 2005, 01:29
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic In the xy-coordinate system, rectangle ABCD is inscribed wit skamal7 10 14 Jul 2013, 21:27
9 ABCD is a rectangle inscribed in a circle. If the length of AB is thr annmary 7 16 Apr 2011, 23:04
Rectangle ABCD is inscribed in circle C. What is the ritula 5 25 Jun 2008, 02:46
In the xy-coordinate system, rectangle ABCD is inscribed kuristar 1 04 May 2006, 08:06
1 Rectangle ABCD is inscribed in a circle as shown above. What cloaked_vessel 9 26 Mar 2005, 08:12
Display posts from previous: Sort by

In the xy-coordinate system, rectangle ABCD is inscribed

  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®.