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Giải bài tập 6.27 trang 24 SGK Toán 9 tập 2 - Kết nối tri thức

Một bể bơi hình chữ nhật có diện tích (300{m^2}) và chu vi là 74m. Tính các kích thước của bể bơi này.

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

Toán - Văn - Anh
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Đề bài

Một bể bơi hình chữ nhật có diện tích \(300{m^2}\) và chu vi là 74m. Tính các kích thước của bể bơi này.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Chiều dài và chiều rộng của bể bơi là nghiệm của phương trình: \({x^2} - 37x + 300 = 0\) + Giải phương trình ta tìm được chiều dài và chiều rộng của bể bơi.

Lời giải chi tiết

Nửa chu vi của mảnh vườn là: \(74:2 = 37\left( m \right)\). Khi đó, chiều dài và chiều rộng của mảnh vườn là nghiệm của phương trình:  \({x^2} - 37x + 300 = 0\) Ta có: \(\Delta  = {\left( { - 37} \right)^2} - 4.1.300 = 169 > 0,\sqrt \Delta   = 13\). Nên phương trình có hai nghiệm phân biệt \({x_1} = \frac{{37 + 13}}{2} = 25;{x_2} = \frac{{37 - 13}}{2} = 12\) Vậy chiều rộng và chiều dài của bể bơi lần lượt là 12m và 25m.

Chú ý khi giải: 🐈Trong hình chữ nhật, chiều dài luôn lớn hơn chiều rộng.

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