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Giải bài 8 trang 42 sách bài tập toán 8 – Cánh diều

Người ta dùng một đoạn dây thép và uốn nó thành hai hình vuoogn \(ABCD,MNPQ\) như Hình 2. Độ dài cạnh hình vuông \(MNPQ\) là \(x\) (cm). Độ dài cạnh hình vuông \(ABCD\) hơn ba lần độ dài cạnh hình vuông \(MNPQ\) là 3 cm

🦄Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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Đề bài

Người ta dùng một đoạn dây thép và uốn nó thành hai hình vuoogn \(ABCD,MNPQ\) như Hình 2. Độ dài cạnh hình vuông \(MNPQ\) là \(x\) (cm). Độ dài cạnh hình vuông \(ABCD\) hơn ba lần độ dài cạnh hình vuông \(MNPQ\) là 3 cm. Sau khi uốn xong còn thừa đoạn dây thép \(ME\) dài 2 cm. Tìm \(x\), biết độ dài đoạn dây thép đã dùng là 62 cm.

Phương pháp giải - Xem chi tiết

Viết biểu thức biểu diễn chu vi hình vuông MNPQ và ABCD. Viết phương trình biểu diễn độ dài đoạn dây thép đã dùng và tìm x.

Lời giải chi tiết

Theo đề bài ta có:Độ dài cạnh hình vuông \(MNPQ\) là \(x\) cm.Độ dài cạnh hình vuông \(ABCD\) là \(\left( {3x + 3} \right)\) cmĐộ dài đoạn dây thép đã dùng là 62 cm.Từ đó ta có phương trình:\(\begin{array}{l}4x + 4\left( {3x + 3} \right) + 2 = 62\\ \Leftrightarrow 4x + 12x + 12 + 2 = 62\\ \Leftrightarrow 16x = 48\\ \Leftrightarrow x = 3\end{array}\)Vậy \(x = 3\).

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