✔ 最佳答案
因為DE//BC,所以△ADE~△ABC
DE : BC = AE : AC = AD : AB
令DE/15 = AE/9 = AD/16 = k
DE = 15k, AE = 9k, AD = 16k
∠FBC = ∠FBD, ∠FBC = ∠BFD
所以∠FBD = ∠BFD 得 BD = FD 同理 CE = FE
所以 DE = FD + FE = BD+CE = (AB - AD) + (AC - AE) = (16 - 16k) + (9 - 9k) = 25 - 25k
因為DE = 15k 又 DE = 25 -25k
15k = 25 - 25k
40k = 25
k = 5/8
DE = 15k = 15*(5/8) = 75/8
故選 (B)
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2014-01-30 19:04:22 補充:
進哥所說 △ADE 周長 = AB+AC
是因為 DB=DF, EC=EF
還有周長比等於邊長比是因為△ADE~△ABC
2014-01-30 19:21:45 補充:
意見區002 進哥大所建議的方法最快,請版主研究參考