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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In the xy-coordinate system, rectangle ABCD is inscribed ##### This topic has 1 expert reply and 0 member replies ### Top Member ## In the xy-coordinate system, rectangle ABCD is inscribed ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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 OA B Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2418 messages Followed by: 349 members Upvotes: 1090 GMAT Score: 780 If a circle has the equation x^2 + y^2 = r^2, then it is a circle centered at the origin, with radius r. So our circle here is a circle of radius 5, centered at (0, 0). So, if a diagonal of the inscribed rectangle lies on the x-axis, the coordinates of its endpoints must be (-5, 0) and (5, 0). We know the line y = 3x + 15 intersects the circle in two points. If we solve that line's equation along with the circle's equation, we'll find where those two points are. Substituting y = 3x + 15 into the circle's equation, we have x^2 + (3x + 15)^2 = 25 x^2 + 9x^2 + 90x + 225 = 25 10x^2 + 90x + 200 = 0 x^2 + 9x + 20 = 0 (x + 4)(x + 5) = 0 and the two intersection points are at x = -5 (which we knew already) and x = -4. The y-coordinate of this second point is 3 (which you can find by plugging x = -4 into either the line's or the circle's equation, or you can notice you'll make a 3-4-5 triangle since the radius is 5). Finally, the diagonal chops the rectangle in half. So the triangle consisting of the points (-5, 0), (5, 0) and (-4, 3) is half of the rectangle. Taking the horizontal edge, along the x-axis, as our base, the length of the base is 10. Then the height is just 3, the y-coordinate of the point above the x-axis. So the area of this triangle is 3*10/2, and that's half the rectangle's area, so the rectangle's area is 30. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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