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Giải bài 13 trang 41 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Cho hình chữ nhật ABCD có diện tích bằng 10 cm2 và tỉ số giữa hai cạnh kề nhau AB : AD = 3:2. Tìm độ dài cạnh AB (kết quả làm tròn đến hàng phần mười của xăngtimet).

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

Toán - Văn - Anh
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Đề bài

Cho hình chữ nhật ABCD có diện tích bằng 10 cm2ꦬ và tỉ số giữa hai cạnh kề nhau AB : AD = 3:2. Tìm độ dài cạnh AB (kết quả làm tròn đến hàng phần mười của xăngtimet).

Phương pháp giải - Xem chi tiết

Đặt x = AB (x > 0).

🍃Dựa vào dữ kiện đề bài để lập công thức diện tích hình chữ nhật ABCD theo x.

Giải tìm x và kết luận.

Lời giải chi tiết

Đặt x = AB (x > 0). Ta có \(\frac{{AB}}{{AD}} = \frac{3}{2}\), suy ra \(AD = \frac{{2AB}}{3} = \frac{{2x}}{3}\). Diện tích hình chữ nhật ABCD là S = AB.AD = \(\frac{{2{x^2}}}{3}\).

Theo đề bài ta có \(\frac{{2{x^2}}}{3} = 10\), suy ra x2ꦬ = 15, suy ra x = \(\sqrt {15}  \approx 3,9\) (cm).

Vậy độ dài cạnh AB là khoảng 3,9 cm.

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