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Giải bài 9.38 trang 60 sách bài tập toán 8 - Kết nối tri thức với cuộc sống

Tìm độ dài cạnh huyền của một tam giác vuông biết rằng tỉ số của độ dài hai cạnh góc vuông là 3:4 và chu vi tam giác bằng 48cm.

🍸Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Tìm độ dài cạnh huyền của một tam giác vuông biết rằng tỉ số của độ dài hai cạnh góc vuông là 3:4 và chu vi tam giác bằng 48cm.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức định lí Pythagore để tính độ dài AB, AC: Trong một tam giác vuông, bình phương cạnh huyền bằng tổng các bình phương của hai cạnh góc vuông.

Lời giải chi tiết

Giả sử tam giác ABC vuông tại A có \(AB:AC = 3:4\) và chu vi tam giác bằng 48cm.Vì \(AB:AC = 3:4\) nên \(AB = \frac{3}{4}AC\)Áp dụng định lí Pythagore vào tam giác ABC vuông tại A có:\(B{C^2} = A{B^2} + A{C^2} = {\left( {\frac{3}{4}AC} \right)^2} + A{C^2} = \frac{{25}}{{16}}A{C^2}\) nên \(BC = \frac{5}{4}AC\)Chu vi tam giác ABC là: \(AB + BC + AC = 48\)\(AC + \frac{3}{4}AC + \frac{5}{4}AC = 48\)\(3AC = 48\)\(AC = 16cm\)Do đó, \(BC = \frac{5}{4}AC = \frac{5}{4}.16 = 20\left( {cm} \right)\)

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