GMAT Club Forum
https://gmatclub.com:443/forum/

In triangle ABC, point X is the midpoint of side AC and
https://gmatclub.com/forum/in-triangle-abc-point-x-is-the-midpoint-of-side-ac-and-89433.html
Page 1 of 1

Author:  burnttwinky [ 19 Jan 2010, 21:04 ]
Post subject:  In triangle ABC, point X is the midpoint of side AC and

In triangle ABC, point X is the midpoint of side AC and point Y is the midpoint of side BC. If point R is the midpoint of line segment XC and if point S is the midpoint of line segment YC, what is the area of triangular region RCS ?

(1) The area of triangular region ABX is 32.
(2) The length of one of the altitudes of triangle ABC is 8.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-triangle-abc-point-x-is-the-midpoint-of-side-ac-and-82671.html

Author:  gurpreetsingh [ 19 Jan 2010, 21:27 ]
Post subject:  Re: OG #12 Problem 109

IMO ans should be A.

Area of triangle ABX = area of BXC as median divides the triangle into 2 equal areas.

similarly area of XYC = 1/2 BXC = ( 1/2 ABX) = 1/2 * 32 = 16

Now XYC and RSC are similar triangles
Since we have area of XYC , we can find the area of triangle RSC.
Thus statement 1 is sufficient.

Statement 2 seems not sufficient, not enough parameters given.

ANS - A.. OA please.

Attachments:
File comment: Image for the problem
test.JPG
test.JPG [ 7.01 KiB | Viewed 7100 times ]

Author:  burnttwinky [ 19 Jan 2010, 21:57 ]
Post subject:  Re: OG #12 Problem 109

You are correct. The official answer is A.

Author:  burnttwinky [ 19 Jan 2010, 22:05 ]
Post subject:  Re: OG #12 Problem 109

Okay, I didn't see that. So, if you draw a line from the vertex of a triangle to the midpoint of an opposite line, does that automatically split the triangle into two smaller equal triangles? If so, the problem makes a lot more sense. Thanks for the explanation.

Author:  gurpreetsingh [ 19 Jan 2010, 22:13 ]
Post subject:  Re: OG #12 Problem 109

Yes the line joining mid point and opp vertex divides it into 2 triangles having equal area.

Area of triangle = 1/2 base * height

since height remains the same and base is divided into 2 equal parts...thus areas are also divided into 2 equal parts..
Letme know if u got the concept else I will elaborate it.

Author:  siddhans [ 02 Jul 2011, 21:41 ]
Post subject:  Re: OG #12 Problem 109

I had one question though .

Since Area of Traingle ABX = Area of Trianglr BXC


Will Area of triangle XYC = 1/2 Area of triangle ABC?

i.e Area of triangle XYC = 1/2 *64 = 32?

and will Area of triangle RCS = 1/4 (Area of triangle ABC)????

therefore, Area of triangle RCS = 1/4 *64 = 16??? Is this correct?


Can someone please verify if what I have done is correct?

Page 1 of 1 All times are UTC - 8 hours
Powered by phpBB © phpBB Group
http://www.phpbb.com/