✔ 最佳答案
圖片參考：
http://img5.imageshack.us/img5/484/40178066.png
1) 設 EF = EC = x ,
則 AE = AF + FE = 4 + x
DE = DC - EC = 4 - x
勾股定理 :
AE^2 = AD^2 + DE^2
(4 + x)^2 = 4^2 + (4 - x)^2
8(2x) = 16
x = 1
△ADE = (1/2) DE * AD = (1/2) (4 - 1) (4) = 6
△ADF = (AF/AE) * △ADE = (4/(4+1)) * 6 = 24/5
2)
圖片參考：
http://img196.imageshack.us/img196/2126/123cez.png
BF + FC = 10 ...........(1)
;
AD = AB + BD = 6 + BF
;
AE = AC + CE = 8 + FC
因 AD = AE ,
故 BF + 6 = FC + 8 .........(2)
(1) - (2) :
FC - 6 = 2 - FC
FC = 4
勾股定理 :
BE^2 = AB^2 + AE^2
BE^2 = 6^2 + (AC + CE)^2
BE^2 = 36 + (AC + FC)^2
BE^2 = 36 + (8 + 4)^2
BE^2 = 180
BE = √180
BE = 6√5
2010-10-27 23:01:29 補充：
一個必須說明的重要事項 :
10^2 = 6^2 + 8^2
BC^2 = AB^2 + AC^2
由勾股逆定理 , ㄥBAC 是直角。
2010-10-27 23:30:57 補充：
不用客氣^^....
