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Giải bài tập 7.16 trang 39 SGK Toán 9 tập 2 - Cùng khám phá

Một tam giác vuông có hiệu độ dài hai cạnh góc vuông là 7 cm. Tính diện tích của tam giác vuông đó biết nó nội tiếp trong đường tròn đường kính 13 cm.

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

Toán - Văn - Anh
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Đề bài

🎶Một tam giác vuông có hiệu độ dài hai cạnh góc vuông là 7 cm. Tính diện tích của tam giác vuông đó biết nó nội tiếp trong đường tròn đường kính 13 cm.

Phương pháp giải - Xem chi tiết

🍌Đường tròn ngoại tiếp tam giác vuông có bán kính bằng nửa cạnh huyền.

Bước 1: Lập phương trình:

Chọn ẩn số và đặt điều kiện cho ẩn số.

ꦐBiểu diễn các đại lượng chưa biết theo ẩn và các đại lượng đã biết.

ꦆLập phương trình biểu thị mối quan hệ giữa các đại lượng.

Bước 2: Giải phương trình.

♏Bước 3: Kiểm tra xem nghiệm có thoả mãn điều kiện của ẩn hay không rồi kết luận.

Lời giải chi tiết

Ta có cạnh huyền có độ dài là 2R bằng đường kính là 13 cm Gọi cạnh góc vuông là x (x > 0) Suy ra cạnh góc vuông còn lại x – 7 (cm) Áp dụng định lí Pythagore vào tam giác vuông ta có: \(\begin{array}{l}{x^2} + {\left( {x - 7} \right)^2} = {13^2}\\2{x^2} - 14x - 120 = 0\end{array}\) Giải phương trình ta được \({x_1} = 12(TM);{x_2} =  - 5(L)\) Vậy độ dài hai cạnh góc vuông là 12 cm và 5 cm. Suy ra diện tích tam giác vuông là: \(\frac{1}{2}.12.5 = 30\)\(c{m^2}\)

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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