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Giải bài tập 4 trang 41 SGK Toán 9 tập 1 - Cánh diều

Tìm (x > 0) sao cho ở Hình 2 chu vi của hình tam giác lớn hơn chu vi của hình chữ nhật:

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

Toán - Văn - Anh
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Đề bài

Tìm \(x > 0\) sao cho ở Hình 2🎐 chu vi của hình tam giác lớn hơn chu vi của hình chữ nhật:

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Viết bất phương trình liên hệ rồi giải bất phương trình.

Lời giải chi tiết

+ Chu vi của hình tam giác là: \(x + 4 + x + 5 + x + 2 = 3x + 11\). + Chu vi của hình chữ nhật là: \(2.\left( {x + 3 + x + 1} \right) = 2\left( {2x + 4} \right) = 4x + 8\). + Để chu vi của hình tam giác lớn hơn chu vi của hình chữ nhật ta có bất phương trình: \(\begin{array}{l}3x + 11 > 4x + 8\\3x + 11 - 4x - 8 > 0\\ - x + 3 > 0\\ - x >  - 3\\x < 3\end{array}\) Mà \(x > 0\) nên ta có \(0 < x < 3\). Vậy \(x \in \left\{ {1;2} \right\}\) thỏa mãn yêu cầu đề bài.

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