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In triangle ABC, point X is the midpoint of side AC and

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burnttwinky
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In triangle ABC, point X is the midpoint of side AC and [#permalink] In triangle ABC, point X is the midpoint of side AC and   Updated on: 11 Jul 2013, 02:29
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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
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A

Originally posted by burnttwinky on 19 Jan 2010, 22:04.
Last edited by Bunuel on 11 Jul 2013, 02:29, edited 1 time in total.
Edited the question and added the OA
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Re: OG #12 Problem 109 [#permalink] In triangle ABC, point X is the midpoint of side AC and   19 Jan 2010, 22:27
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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.
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burnttwinky
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Re: OG #12 Problem 109 [#permalink] In triangle ABC, point X is the midpoint of side AC and   19 Jan 2010, 22:57
You are correct. The official answer is A.
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Re: OG #12 Problem 109 [#permalink] In triangle ABC, point X is the midpoint of side AC and   19 Jan 2010, 23:05
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.
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Re: OG #12 Problem 109 [#permalink] In triangle ABC, point X is the midpoint of side AC and   19 Jan 2010, 23:13
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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.
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Re: OG #12 Problem 109 [#permalink] In triangle ABC, point X is the midpoint of side AC and   02 Jul 2011, 22:41
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?
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Re: OG #12 Problem 109 [#permalink]
02 Jul 2011, 22:41
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