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Giải bài tập 4 trang 78 SGK Toán 9 tập 2 - Cánh diều

Mặt trên của tấm đệm có dạng hình tròn ở Hình 29 gợi nên hình ảnh đường tròn ngoại tiếp hình chữ nhật. Biết hình chữ nhật đó có chiều rộng, chiều dài lần lượt là 3 dm, 5 dm. Tính độ dài đường kính mặt trên của tấm đệm, từ đó tính diện tích mặt trên của tấm đệm.

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

Toán - Văn - Anh
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Đề bài

Mặt trên của tấm đệm có dạng hình tròn ở Hình 29 gợi nên hình ảnh đường tròn ngoại tiếp hình chữ nhật. Biết hình chữ nhật đó có chiều rộng, chiều dài lần lượt là 3 dm, 5 dm. Tính độ dài đường kính mặt trên của tấm đệm, từ đó tính diện tích mặt trên của tấm đệm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Bước 1: Áp dụng Định lý Pytago trong tam giác vuông ACB để tính đường kính AC. Bước 2: Áp dụng công thức \(S = \pi .\frac{{{d^2}}}{4}.\)

Lời giải chi tiết

Mặt trên của tấm nệm được biểu diễn bằng hình học như sau:

Hình chữ nhật ABCD có chiều dài AB = 5 dm, chiều rộng BC = 3 dm. Xét tam giác ACB vuông tại B có:  \(\begin{array}{l}A{B^2} + B{C^2} = A{C^2}(Pytago)\\{5^2} + {3^2} = A{C^2}\\AC = \sqrt {34} dm\end{array}\) Mà hình chữ nhật ABCD nội tiếp đường tròn nên đường kính tấm đệm là \(AC = \sqrt {34} dm.\) Diện tích hình tròn là: \(S = \pi .\frac{{{d^2}}}{4} = \pi .\frac{{{{\sqrt {34} }^2}}}{4} = \frac{{17\pi }}{2}d{m^2}.\)

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