Cho tam giác ABC.Trên AC lấy điểm M sao cho AM=1/4 AC.Trên BC lấy N sao cho diện tích MCN bằng diện tích AMNB.Tính BN/BC
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Chọn điểm N trên BC và giả sử S_MCN=S_AMNB.
Nối AN.
Do AM=1/4AC hay AM=1/3MC
Ta có: S_MNC=3S_AMN (MC=3AM, chung đường cao từ N)
Để S_AMNB=SMNC thì S_ANB=(3-1)S_AMN=2S_AMN
Diện tích ABC có 3+1+2=6 (phần) thì S_ANB có 2 phần hay S_ANB=1/3S_ABC.
Suy ra: BN=1/3BC
máy mình bị lỗi phần vẽ hình bạn tự vẽ nhé
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Nối B với N
Xét tam giác BNC và NMC
- Chung chiều cao hạ từ đỉnh N xuống BC
- MC = 3 lần BC
=> SNMC = 3 lần SBNC = 15 X 3 = 45 ( cm2 )
Xét 2 tam giác ABC và BNC
- Chung chiều cao hạ từ đỉnh B xuống cạnh AC
- NC = 3 lần AC
=> SABC = SBNC X 3 = 45 X 3 = 135 ( CM2 )
Đáp số : 135 cm2
Nối B với N
Xét tam giác BNC và NMC
- Chung chiều cao hạ từ đỉnh N xuống BC
- MC = 3 lần BC
=> SNMC = 3 lần SBNC = 15 X 3 = 45 ( cm2 )
Xét 2 tam giác ABC và BNC
- Chung chiều cao hạ từ đỉnh B xuống cạnh AC
- NC = 3 lần AC
=> SABC = SBNC X 3 = 45 X 3 = 135 ( CM2 )
Đáp số : 135 cm2