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 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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Official Answer

A

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gurpreetsingh · Answer

IMO ans should be A.

Area of triangle ABX = area of BXC as median divides the triangle into 2 equal areas.

similarly area of XYC = 1/2 BXC = ( 1/2 ABX) = 1/2 * 32 = 16

Now XYC and RSC are similar triangles
Since we have area of XYC , we can find the area of triangle RSC.
Thus statement 1 is sufficient.

Statement 2 seems not sufficient, not enough parameters given.

ANS - A.. OA please.

burnttwinky · Answer

You are correct. The official answer is A.

burnttwinky · Answer

Okay, I didn't see that. So, if you draw a line from the vertex of a triangle to the midpoint of an opposite line, does that automatically split the triangle into two smaller equal triangles? If so, the problem makes a lot more sense. Thanks for the explanation.

gurpreetsingh · Answer

Yes the line joining mid point and opp vertex divides it into 2 triangles having equal area.

Area of triangle = 1/2 base * height

since height remains the same and base is divided into 2 equal parts...thus areas are also divided into 2 equal parts..
Letme know if u got the concept else I will elaborate it.

siddhans · Answer

I had one question though .

Since Area of Traingle ABX = Area of Trianglr BXC

Will Area of triangle XYC = 1/2 Area of triangle ABC?

i.e Area of triangle XYC = 1/2 *64 = 32?

and will Area of triangle RCS = 1/4 (Area of triangle ABC)????

therefore, Area of triangle RCS = 1/4 *64 = 16??? Is this correct?

Can someone please verify if what I have done is correct?

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

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

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