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06 Nov 2018, 01:28
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A
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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.
(1) The area of the triangular region ABP is 40.
(2) The length of one of the altitudes of triangle ABC is 12.
06 Nov 2018, 01:42
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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.
Answer: A
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.
Answer: A
01 Dec 2018, 03:49
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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
Bunnel and other experts posted great detailed solution for similar problem in the above link.
Hope it helps
