GWD 21 22

不知不觉

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

LunarLin

我觉得答案应该是A（1满足，2不满足）

smileday

why (1) is sufficient?

any reasonable principle or formulation to prove ?

paulineliao

can anybody explain that?

yaoyao99

XYC = 0.5 * area of BXC = 0.5 * area of ABX (same height, half the base)

RS // XY => area of RSC = 0.25 * area of XYC

smileday

以下是引用yaoyao99在2006-6-16 9:02:00的发言：

XYC = 0.5 * area of BXC = 0.5 * area of ABX (same height, half the base)--(1)

RS // XY => area of RSC = 0.25 * area of XYC--(2)

from your (1),

we got : area of XYC=1/4 area of ABC,
    

but, I don't got the idea -your (2):

 

 

 

yaoyao99

Based on the condition, the height is 1:2, base is also 1:2 => area is 1/4

smileday

allow my stupid,pls,

why we know lineRS=1/2(lineXY) ?

thank you...

smileday

ding..

hitlzc

http://forum.chasedream.com/dispbbs.asp?boardid=22&replyid=1398556&id=150288&page=1&skin=0&Star=2

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