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

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Manager
Joined: 09 Sep 2004
Posts: 54
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In triangle ABC, point X is the midpoint of side AC and [#permalink]  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.
Director
Joined: 16 Jun 2004
Posts: 893
Followers: 2

Kudos [?]: 19 [0], given: 0

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.
Director
Joined: 20 Jul 2004
Posts: 593
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Kudos [?]: 48 [0], given: 0

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
Joined: 07 Oct 2003
Posts: 358
Location: Manhattan
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what is the OA here, and more importantly, what's the area of triang. RCS?
Joined: 31 Dec 1969
Location: India
Concentration: General Management, Strategy
GMAT 1: 710 Q49 V0
GMAT 2: 740 Q40 V50
GMAT 3: 700 Q48 V38
GPA: 3.6
Followers: 0

Kudos [?]: 89 [0], given: 87116

totally agree: the answer is 4..... thanks for the question, i'm forgetting triangles properties....

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