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

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Joined: 11 May 2008
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In triangle ABC, point X is the midpoint of side AC and  [#permalink]

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01 Aug 2008, 04:27
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 triangle region RCS
(1) the area of triangular region ABX is 32
(2) the length of one of the altitudes of triangle ABC is 8
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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01 Aug 2008, 04:45
Senior Manager
Joined: 16 Jul 2008
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01 Aug 2008, 05:29
1
I am almost sure that the first statement is sufficient, but have no idea what to do with the second one... So I'd go for A
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02 Aug 2008, 23:53
arjtryarjtry wrote:
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 triangle region RCS
(1) the area of triangular region ABX is 32
(2) the length of one of the altitudes of triangle ABC is 8
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO A
given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.
(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles
(2) does not indicate are but just the altitude hence cant help in finding are of RCS

(1) is suffi and (2) is not

IMO A
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Joined: 09 Jul 2007
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05 Aug 2008, 16:21
IMO A .
Reason : as ACB and RCS are symitrical triangles, there sides will be proportionate ( ratio 1:4 ).. and so area will be also propotionate , but with a square.. i.e 1: 16.. as the area of ACB is 64 as per statement 1, the area of RCS it bill be 4.
statement 2 is not sufficient as the altitue can be any of the 3.
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Joined: 18 Jul 2008
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05 Aug 2008, 18:01
Question on similar triangles -

What are the requirements? I thought you needed two angles to tell that 2 triangles are similar?
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Joined: 07 Nov 2007
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06 Aug 2008, 10:13
spriya wrote:
arjtryarjtry wrote:
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 triangle region RCS
(1) the area of triangular region ABX is 32
(2) the length of one of the altitudes of triangle ABC is 8
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO A
given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.
(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles
(2) does not indicate are but just the altitude hence cant help in finding are of RCS

(1) is suffi and (2) is not

IMO A

How come BCX similar to ABC?
I agree that RCS is similar to ABC.

Given ABX=32.. is it possible to find ABC area?
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Joined: 31 Jul 2008
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06 Aug 2008, 15:22
Here the triangles are similar as :

1 vertex (angle is common)
2 base is parallel (which suggests equal angles)

Hence A shud be the choice
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07 Aug 2008, 07:44
stallone wrote:
Here the triangles are similar as :

1 vertex (angle is common)
2 base is parallel (which suggests equal angles)

Hence A shud be the choice

I agree that triangle ABC is similar to triangle RCS.

But ABX is not similar to RCS.

my question is in statement 1 given ABX area not ABC.
to find the RCS we need ABC are which is similar to RCS

am i missing something???
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Joined: 22 Jul 2008
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07 Aug 2008, 10:08
given that RCS is similar to YXC ,YXC is similar to BCX which is similar to ABC.
(1) gives area of ABX which can be used to get area of RCS since these are all similar triangles
(2) does not indicate are but just the altitude hence cant help in finding are of RCS

HOW does YXC be similiar to BCX and ABX to RCS

I am confused
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Joined: 07 Aug 2008
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07 Aug 2008, 10:43
option 1 is sufficient.

From the area of ABX, we can find the area of RCS, so statement "1" is sufficient
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07 Aug 2008, 12:53
farrukhiq wrote:
option 1 is sufficient.

From the area of ABX, we can find the area of RCS, so statement "1" is sufficient

Can you exlaborate how to find RCS from ABX
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Joined: 08 Aug 2008
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08 Aug 2008, 06:46
agreed RCS similar to ABC....but ABX cannot be concluded to be simlar to ABC.
1) altitude BX
2)AX=1/2AC
3)angle?

/_A cant be considered as there is no SSA or ASS similarity.
please correct me if im missing something else.....

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: spoilt my head over this one &nbs [#permalink] 08 Aug 2008, 06:46
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# In triangle ABC, point X is the midpoint of side AC and

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