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Giải bài 6 trang 93 vở thực hành Toán 9 tập 2

Người ta muốn làm một khung gỗ tam giác đều để đặt vừa khít một chiếc đồng hồ hình tròn có đường kính 30cm như hình bên. Hỏi độ dài các cạnh (phía bên trong) của khung gỗ phải bằng bao nhiêu?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Người ta muốn làm một khung gỗ tam giác đều để đặt vừa khít một chiếc đồng hồ hình tròn có đường kính 30cm như hình bên. Hỏi độ dài các cạnh (phía bên trong) của khung gỗ phải bằng bao nhiêu?

Phương pháp giải - Xem chi tiết

+ Gọi tam giác tạo bởi các cạnh bên trong khung gỗ là tam giác đều ABC có cạnh bằng a. + Tính được bán kính r đường tròn nội tiếp tam giác ABC. + Ta có: \(r = \frac{{\sqrt 3 }}{6}a\), từ đó tính được độ dài cạnh của tam giác ABC.

Lời giải chi tiết

Gọi tam giác tạo bởi các cạnh bên trong khung gỗ là tam giác đều ABC có cạnh bằng a. Khi đó đường tròn nội tiếp tam giác này có bán kính bằng \(r = \frac{{30}}{2} = 15\left( {cm} \right)\). Mặt khác, \(r = \frac{{\sqrt 3 }}{6}a\). Suy ra \(a = \frac{6}{{\sqrt 3 }}r = 30\sqrt 3 \left( {cm} \right)\).

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