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Giải bài tập 5 trang 21 SGK Toán 9 tập 2 - Chân trời sáng tạo

Một mảnh vườn hình chữ nhật chu vi là 116 m, diện tích 805 m2. Tìm chiều dài và chiều rộng của mảnh vườn đó?

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

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Đề bài

Một mảnh vườn hình chữ nhật chu vi là 116 m, diện tích 805 m2. Tìm chiều dài và chiều rộng của mảnh vườn đó?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Gọi ẩn \({x_1},{x_2}\) lần lượt là chiều dài và chiều rộng của khu vườn.

Lập phương trình ẩn \({x_1},{x_2}\) theo chu vi và diện tích.

Dựa vào: Nếu hai số có tổng bằng S và tích bằng P thì hai số đó là nghiệm của phương trình \({x^2} - Sx + P = 0\) tìm chiều dài và chiều rộng.

Lời giải chi tiết

Gọi \({x_1},{x_2}\) lần lượt là chiều dài và chiều rộng của khu vườn. Nửa chu vi là \(\frac{{116}}{2} = 58\) m hay \({x_1} + {x_2} = 58\).

Diện tích 805 m2 hay \({x_1}.{x_2} = 805\)

\({x_1},{x_2}\) là nghiệm của phương trình \({x^2} - 58x + 805 = 0\) Ta có \(\Delta  = {\left( { - 58} \right)^2} - 4.1.805 = 144 > 0;\sqrt \Delta   = \sqrt {144}  = 12\) suy ra \({x_1} = \frac{{58 + 12}}{2} = 35;{x_2} = \frac{{58 - 12}}{2} = 23\). Vậy chiều dài khu vườn là 35 m và chiều rộng là 23 m.

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