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Giải bài 9 trang 81 sách bài tập toán 10 - Chân trời sáng tạo

Tam giác ABC có diện tích S. Nếu tăng cạnh BC lên 2 lần đồng thời tăng cạnh CA lên 3 lần và giữ nguyên độ lớn góc C thì khi đó diện tích của tam giác mới được tạo nên bằng:

👍Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Tam giác ABC có diện tích S. Nếu tăng cạnh BC lên 2 lần đồng thời tăng cạnh CA lên 3 lần và giữ nguyên độ lớn góc C ෴thì khi đó diện tích của tam giác mới được tạo nên bằng:

A. 2S  

B. 3S 

C. 4S   

D. 6S

Lời giải chi tiết

Trước khi tăng ta có diện tích tam giác \({S_{ABC}} = \frac{1}{2}BC.CA.\sin C\)Sau khi tăng ta có: \(B'C = 2BC,CA' = 3CA\), suy ra diện tích tam giác sau khi tăng là                   \({S_{A'B'C}} = \frac{1}{2}B'C.A'C\sin C = \frac{1}{2}.2BC.3CA.\sin C = 6{S_{ABC}}\)Chọn D

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