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Giải bài 5 trang 12 sách bài tập toán 9 - Chân trời sáng tạo tập 2

Bác Thanh có một mảnh đất hình chữ nhật với chiều rộng bằng (frac{2}{3}) chiều dài. Do quy hoạch mở rộng đường nên chiều dài và chiều rộng mảnh đất đều giảm đi 5 m, do đó diện tích mảnh đất còn lại chỉ bằng 84% diện tích lúc đầu. Tính diện tích mảnh đất lúc đầu.

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

Toán - Văn - Anh
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Đề bài

Bác Thanh có một mảnh đất hình chữ nhật với chiều rộng bằng \(\frac{2}{3}\) chiều dài. Do quy hoạch mở rộng đường nên chiều dài và chiều rộng mảnh đất đều giảm đi 5 m, do đó diện tích mảnh đất còn lại chỉ bằng 84% diện tích lúc đầu. Tính diện tích mảnh đất lúc đầu.

Phương pháp giải - Xem chi tiết

Gọi x (km/h) là tốc độ của tàu chở hàng (x > 3). Dựa vào dữ kiện đề bài để lập phương trình bậc hai. Giải phương trình và kết luận.

Lời giải chi tiết

🐷Gọi x (m) là chiều dài mảnh đất lúc đầu (x > 5).

Chiều rộng của mảnh đất lúc đầu là \(\frac{2}{3}x\) (m).

Chiều dài của mảnh đất sau khi giảm là x – 5 (m).

Chiều rộng của mảnh đất sau khi giảm là \(\frac{2}{3}x\) – 5 (m).

ꦉDiện tích mảnh đất còn lại bằng 84% diện tích lúc đầu nên ta có phương trình:

🎉\(\left( {x - 5} \right)\left( {\frac{2}{3}x - 5} \right) = 84\% .\frac{2}{3}{x^2}\)

Giải phương trình trên, ta được \({x_1} = 75\) (thoả mãn); \({x_2} = \frac{{25}}{8}\) (loại).

💙Vậy mảnh đất lúc đầu có chiều dài là 75 m, chiều rộng là 50 m.

Diện tích mảnh đất lúc đầu là 3750 m2.

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