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Better explanations than the OG?

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by winniethepooh » Sat Jul 23, 2011 1:10 pm
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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by goalevan » Sat Jul 23, 2011 2:14 pm
The OG explanation adds several triangles to the drawing that are unnecessary. The complete triangle ABC has area (1/2)B*H, and since triangle RCS is created by cutting the base and the height in half twice, it has an area of (1/2)(1/4B)(1/4H) = BH/32. Thus we only need the value of the product BH to solve for RCS's area. "BH = ?"

Statement 1) Area of region ABX = 32, so (1/2)(1/2B)(H) = 32, and BH/4 = 32, so BH = 128. Sufficient.

Statement 2) H = 8, but we are not given any information about B. Insufficient.

A
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by MBA.Aspirant » Sat Jul 23, 2011 3:33 pm
A is sufficient

Since area of ABX = 32, then area of ABC is 32 * 2 = 64

triangles ABC and RSC are similar (having one common angle and proportional sides)

RC/AC = 1/4

Area of RSC/area of ABC = 1/16

1:16
x:64

x = 4
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