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

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
In triangle ABC, point P is the midpoint of side AC and point Q is the  [#permalink]

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06 Nov 2018, 01:28
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Difficulty:

75% (hard)

Question Stats:

47% (02:11) correct 53% (02:10) wrong based on 43 sessions

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In triangle ABC, point P is the midpoint of side AC and point Q is the midpoint of side BC. If point R is the midpoint of line segment PC and if point S is the midpoint of line segment QC, what is the area of the triangular region CRS ?

(1) The area of the triangular region ABP is 40.
(2) The length of one of the altitudes of triangle ABC is 12.

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Manager
Joined: 08 Sep 2008
Posts: 123
Location: India
Concentration: Operations, General Management
Schools: ISB '20
GPA: 3.8
WE: Operations (Transportation)
Re: In triangle ABC, point P is the midpoint of side AC and point Q is the  [#permalink]

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06 Nov 2018, 01:42
2
P- Mid point of AC—and R mid point of PC
Means RC is ¼ of AC
Q- Mid point of BC—and S is mid point of BC
Means SC is ¼ of BC.
Triangle RSC , QPC and ABC are similar
We know in similar figures
A1/A2 = (Length of side of figure 1 / Length of side of figure 2 ) ^2

A1/ A2 = (¼) ^2= 1/16
Statement 1: Area of ABP is 40.
Area of ABC= 80
We can find out area of CRS. i.e. 80 *(1/16). Sufficient.

Statement 2:
The length of one of the altitudes of triangle ABC is 12.
NO information about Base. To find out area.
Not sufficient.

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Vishal

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Manager
Joined: 05 Oct 2017
Posts: 66
Location: India
Schools: GWU '21, Isenberg'21
Re: In triangle ABC, point P is the midpoint of side AC and point Q is the  [#permalink]

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01 Dec 2018, 03:49
1
https://gmatclub.com/forum/in-triangle-abc-point-x-is-the-midpoint-of-side-ac-and-82671.html

Bunnel and other experts posted great detailed solution for similar problem in the above link.

Hope it helps
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Re: In triangle ABC, point P is the midpoint of side AC and point Q is the   [#permalink] 01 Dec 2018, 03:49
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