GEOMETRY - TRIANGLES

[amitdgr]

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


No idea what the answer is...

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[stubbornp]

bcoz both are similar triangles...area should be one fourth of original..

stmt 1-correct...

stmt2-insufficient-

A

[amitdgr]

bcoz both are similar triangles...area should be one fourth of original..

stmt 1-correct...

stmt2-insufficient-

A

which "both" are similar triangles ?

Thanks

[stubbornp]

rsc and abc....

[amitdgr]

But nowhere we are given the area of triangle ABC , And the question is asking for area of RCS

[4meonly]

area of ∆ABC is twice the are of ∆ABX
height the same, base of ∆ABC is twice the base of ∆ABX

(1) the area of triangular region ABX is 32
we can find the area of ∆ABC, it is is twice the are of ∆ABX,
so area of ∆ABC is 64

sides of ∆ABC are 4 times the sides of ∆RSC
so the area of ∆ABC is 4^2=16 times more the the area of ∆RSC

64/16=4
the area of ∆RSC is 4

Answer A

[tendays2go]

correct and bravo 4meonly!
i missed the point that height is same for both ABX and ABC
(but, do explain this in the first post only...will save tiny li'l time )
hope i dont repeat this "slip" in the actual exam :O

[amitdgr]

Thanks for explanation 4meonly.

but median is not always the altitude except in equilateral or isoceles triangles, and we are not sure if the triangle at hand is equilateral or isoceles.

Am I missing something ?

[4meonly]

I hope this small picture will help to deal with any problems

[amitdgr]

Thanks Things pretty clear now