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Giải bài 3.1 trang 58 SGK Toán 8 - Cùng khám phá

Tam giác DEF được vẽ trên giấy kẻ ô vuông
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Đề bài

Tam giác DEF được vẽ trên giấy kẻ ô vuông (độ dài cạnh của ô vuông bằng 1) như trong hình 3.10. Tính độ dài cạnh của tam giác DEF.

 

Phương pháp giải - Xem chi tiết

Sử dụng định lí Pythagore tính cạnh huyền trong ba tam giác vuông chứa ba cạnh tam giác DEF.

Lời giải chi tiết

Ta có:Xét tam giác ADE vuông tại A có:\(A{D^2} + A{E^2} = D{E^2}\) (Định lí Pythagore)\( \Rightarrow D{E^2} = {3^2} + {4^2} = 25 \Rightarrow DE = 5\)Xét tam giác BDF vuông tại B có:\(D{F^2} = D{B^2} + B{F^2}\)(Định lí Pythagore)\(D{F^2} = {6^2} + {3^2} = 45 \Rightarrow DF = 3\sqrt 5 \)Xét tam giác CFE vuông tại C có:\(F{E^2} = C{E^2} + C{F^2}\)(Định lí Pythagore)\(F{E^2} = {2^2} + {1^2} = 5 \Rightarrow FE = \sqrt 5 \)

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