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Giải bài 6 trang 72 sách bài tập toán 8 - Chân trời sáng tạo

Trong hình chữ nhật có chu vi 100m, hình nào có diện tích lớn nhất? Tính diện tích đó.

🐓Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Trong hình chữ nhật có chu vi 100m, hình nào có diện tích lớn nhất? Tính diện tích đó.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về diện tích hình chữ nhật để chứng minh: Diện tích hình chữ nhật bằng tích hai kích thước của hình chữ nhật.

Lời giải chi tiết

Gọi một kích thước của hình chữ nhật là x \(\left( {m,x > 0} \right)\) thì kích thước còn lại của hình chữ nhật là: \(50 - x\left( m \right)\)Diện tích của hình chữ nhật là: \(x\left( {50 - x} \right) =  - {x^2} + 50x =  - {\left( {x - 25} \right)^2} + 625 \le 625\)Dấu “=” xảy ra khi: \(x - 25 = 0\) nên \(x = 25\left( {tm} \right)\)Vậy diện tích hình chữ nhật lớn nhất bằng \(625{m^2}\) khi hình chữ nhật là hình vuông có cạnh dài 25m.

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