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

 It is currently 19 Apr 2015, 07:42

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

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the xy-coordinate system, rectangle ABCD is inscribed

Author Message
TAGS:
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 183 [0], given: 0

In the xy-coordinate system, rectangle ABCD is inscribed [#permalink]  23 Mar 2005, 23:37
00:00

Difficulty:

(N/A)

Question Stats:

100% (01:03) correct 0% (00:00) wrong based on 2 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
Joined: 19 Nov 2004
Posts: 284
Location: Germany
Followers: 1

Kudos [?]: 12 [0], given: 0

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]

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

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

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
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 183 [0], given: 0

any other takers ???
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 183 [0], given: 0

both of you are right, the answer is 30.
Similar topics Replies Last post
Similar
Topics:
In the xy-coordinate system, rectangle ABCD is inscribed wit 0 29 Oct 2014, 07:55
9 ABCD is a rectangle inscribed in a circle. If the length of AB is thr 7 16 Apr 2011, 23:04
34 In the xy-coordinate system, rectangle ABCD is inscribed within a circ 20 24 Mar 2011, 21:59
Rectangle ABCD is inscribed in circle C. What is the 5 25 Jun 2008, 02:46
In the xy-coordinate system, rectangle ABCD is inscribed 1 04 May 2006, 08:06
Display posts from previous: Sort by