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

Question

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.

arjtryarjtry · Answer

hmmm, had got the same...

Nerdboy · Answer

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

spriya · Answer

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

ssandeepan · Answer

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.

bigfernhead · Answer

Question on similar triangles -

What are the requirements? I thought you needed two angles to tell that 2 triangles are similar?

x2suresh · Answer

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

Given ABX=32.. is it possible to find ABC area?

stallone · Answer

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

x2suresh · Answer

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???

rnemani · Answer

In an earlier reply :
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

farrukhiq · Answer

option 1 is sufficient.

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

x2suresh · Answer

Can you exlaborate how to find RCS from ABX

prasun84 · Answer

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.....

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

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