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Giải bài 3.2 trang 58 SGK Toán 8 - Cùng khám phá

Tính độ dài đường cao của một tam giác đều có độ dài cạnh bằng
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Đề bài

Tính độ dài đường cao của một tam giác đều có độ dài cạnh bằng \(4cm.\)

Phương pháp giải - Xem chi tiết

Đường cao trong tam giác đều cũng đồng thời là đường trung tuyến. Sử dụng định lí Pythagore để tính độ dài đường cao đó.

Lời giải chi tiết

Cho tam giác ABC đều có độ dài cạnh bằng \(4\,cm.\) Kẻ \(BE \bot AC\)BE vừa là đường cao đồng thời là đường trung tuyến của tam giác ABC.Suy ra E là trung điểm của AC \( \Rightarrow AE = EC = 2cm\)Xét tam giác ABE vuông tại E có\(A{E^2} + B{E^2} = A{B^2}\)(Pythagore)\(\begin{array}{l} \Rightarrow {2^2} + B{E^2} = {4^2} \Rightarrow B{E^2} = 16 - 4 = 12\\ \Rightarrow BE = 2\sqrt 3 \left( {cm} \right)\end{array}\)Vậy độ dài đường cao của một tam giác đều có độ dài cạnh bằng \(4cm\) là \(2\sqrt 3 cm\)

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