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

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Manager
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In triangle ABC, point X is the midpoint of side AC and [#permalink]

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12 Sep 2004, 00:41
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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.
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12 Sep 2004, 09:10
My answer would be A.

First lets go to stem 2: Insufficient because we do not which of the potential 3 altitudes is 8.

From stem 1: From stem 1, we can deduce the following.

a. Area of triangle ABX = 32. Therefore Area of triangle ABC = 64 (since X is the midpoint of AC and BX bisects the area of triangle ABC)

=> Area of BXC = 32. Again since XY bisects BC, Area of XYC = 1/2 of 32 = 16.

=> Again since RS bisects XYC Area of RSC = 8.
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12 Sep 2004, 15:07
My answer is also A, but the area of RCS is 4.

Area ABX = 32.
Therefore, Area ACB = 64 (since X is the midpoint of AC and height would double for the bigger triangle ACB)
Area RCS = Area XCY/4 = Area ACB/16 = 64/16 = 4
Senior Manager
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21 Oct 2004, 09:50
what is the OA here, and more importantly, what's the area of triang. RCS?
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21 Oct 2004, 14:54
totally agree: the answer is 4..... thanks for the question, i'm forgetting triangles properties....

21 Oct 2004, 14:54
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# In triangle ABC, point X is the midpoint of side AC and

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