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Giải bài 5 trang 100 vở thực hành Toán 9 tập 2

Tính diện tích của một hình chữ nhật, biết rằng hình chữ nhật đó có chiều dài gấp hai lần chiều rộng và bán kính đường tròn ngoại tiếp bằng 2,5cm.

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

Toán - Văn - Anh
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Đề bài

Tính diện tích của một hình chữ nhật, biết rằng hình chữ nhật đó có chiều dài gấp hai lần chiều rộng và bán kính đường tròn ngoại tiếp bằng 2,5cm.

Phương pháp giải - Xem chi tiết

+ Xét hình chữ nhật ABCD có \(AB = 2CB\) nội tiếp đường tròn (O). + Bán kính đường tròn ngoại tiếp 2,5cm nên đường chéo của hình chữ nhật bằng 5cm. + Áp dụng định lí Pythagore vào tam giác ABC vuông tại B tính được AB, BC. + Diện tích hình chữ nhật ABCD là: \(S = AB.BC\).

Lời giải chi tiết

Gọi hình chữ nhật đó là ABCD với \(AB = 2BC\). Khi đó, \(AC = 2.2,5 = 5\left( {cm} \right)\). Theo định lí Pythagore cho \(\Delta \)ABC vuông tại B, ta có: \(A{C^2} = A{B^2} + B{C^2} = 5B{C^2}\). Do đó, \(BC = \frac{5}{{\sqrt 5 }} = \sqrt 5 \left( {cm} \right)\); \(AB = 2BC = 2\sqrt 5 \left( {cm} \right)\). Hình chữ nhật ABCD có diện tích là: \({S_{ABCD}} = AB.BC = 10\left( {c{m^2}} \right)\).

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

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