In the xy-coordinate system, rectangle ABCD is inscribed

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Mon Nov 26, 2018 2:40 pm

Timer

00:00

Answers

Stats

Difficulty—

0% CorrectAvg —

0% IncorrectAvg —

Source: GMAT Prep

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

The OA is B

Like this post

Source: Beat The GMAT — Problem Solving | Mon Nov 26, 2018 2:40 pm

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon Nov 26, 2018 11:09 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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

The OA is B

Pl. see the image which is self-explanatory.

Given that the equation of the circle is x^2 + y^2 = 25, we have the radius of the circle = âˆš25 = 5 and the coordinate of the center of the circle = (0, 0). Thus, AC = diameter = 10.

Area of the rectangle ABCD = 2*Area of the triangle ABC = 2*(1/2*BB'*AC) = BB'*10 = 10y.

We have to get the value of y coordinate of point B.

Since point B is at the circle as well as on the line BC (y = 3x + 15), the coordinate of point B would satisfy both.

Plugging-in y = 3x + 15 in x^2 + y^2 = 25, we get

x^2 + (3x + 15)^2 = 25
x^2 + 9x^2 + 90x + 225 = 25
10x^2 + 90x + 200 = 0
x^2 + 9x + 20 = 0
x^2 + 5x + 4x + 20 = 0

x(x + 5) + 4(x + 5) = 0

(x + 5)(x + 4) = 0
x = - 5 or -4

=> The corresponding values of y are 0 and 3.

Thus, there are two points that lie on the line BC and the circle and their coordinates are (-5, 0) and (-4, 3).
Since it is given that point B lies on the II quadrant, the coordinates of point B would be (-4, 3). This given y = 3

Area of the rectangle ABCD = 10y = 10*3 = 30.

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Dilsukhnagar | Hyderabad GMAT Prep | Bangalore GMAT Courses | Kukatpally GRE Prep | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review