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Giải bài 16 trang 27 sách bài tập toán 8 - Chân trời sáng tạo

Ở hình bên, độ dài các cạnh AB, BC và GH được cho theo a và b; hai cạnh CD và EF bằng nhau; ba cạnh AH, GF và ED bằng nhau.

♔Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Ở hình bên, độ dài các cạnh AB, BC và GH được cho theo a và b; hai cạnh CD và EF bằng nhau; ba cạnh AH, GF và ED bằng nhau. a) Tìm độ dài các cạnh AH, GF, ED. b) Tìm độ dài các cạnh CD, EF. c) Tính chu vi của hình bên.

Phương pháp giải - Xem chi tiết

- Sử dụng kiến thức chia hai phân thức để tính: Muốn chia phân thức \(\frac{A}{B}\) cho phân thức \(\frac{C}{D}\) (C khác đa thức không), ta nhân phân thức \(\frac{A}{B}\) với phân thức \(\frac{D}{C}\): \(\frac{A}{B}:\frac{C}{D} = \frac{A}{B}.\frac{D}{C}\) - Sử dụng kiến thức cộng trừ hai đa thức để tính: + Viết hai đa thức trong ngoặc nối với nhau bằng dấu cộng (+) hay trừ (–). + Bỏ dấu ngoặc rồi thu gọn đa thức thu được.

Lời giải chi tiết

a) Ta có: \(AH = GF = ED = \frac{{BC}}{3} = \frac{{9a + 12b}}{3} = \frac{{3\left( {3a + 4b} \right)}}{3} = 3a + 4b\);b) Ta có: \(CD = FE = \frac{{AB - GH}}{2} = \frac{{\left( {6a + 5b} \right) - \left( {2a + 3b} \right)}}{2} = \frac{{4a + 2b}}{2} = \frac{{2\left( {2a + b} \right)}}{2} = 2a + b\)c) Chu vi của hình trên là:\(AB + BC + CD + DE + FE + GF + GH + AH = AB + BC + AB + BC\)\( = 6a + 5b + 9a + 12b + 9a + 12b + 6a + 5b\)\( = \left( {6a + 6a + 9a + 9a} \right) + \left( {5b + 12b + 12b + 5b} \right) = 30a + 34b\)

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