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Giải bài 8 trang 51 sách bài tập toán 9 - Chân trời sáng tạo tập 1

Một phần khung của một cây cầu gồm các thanh thép tạo thành các tam giác vuông cân như Hình 2. Biết rằng cạnh CD có độ dài a (m). Tính độ dài của đoạn BF theo a.

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

Toán - Văn - Anh
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Đề bài

Một phần khung của một cây cầu gồm các thanh thép tạo thành các tam giác vuông cân như Hình 2. Biết rằng cạnh CD có độ dài a (m). Tính độ dài của đoạn BF theo a.

Phương pháp giải - Xem chi tiết

Dựa vào: Định lý Pytago để tính AD, AE và AF. Từ đó: tính BF = AB + AF.

Lời giải chi tiết

Ta có: AD = \(\sqrt {A{C^2} + C{D^2}}  = \sqrt {2C{D^2}}  = CD\sqrt 2  = a\sqrt 2  (m).\) Tương tự, tính được: \(AE = AD\sqrt 2  = 2a (m)\); AF = AE\(\sqrt 2  = 2a\sqrt 2 (m)\) \(AB = \frac{{AC}}{{\sqrt 2 }} = \frac{a}{{\sqrt 2 }} = \frac{{a\sqrt 2 }}{2}(m)\). Từ đó, \(BF = AB + AF = \frac{{a\sqrt 2 }}{2} + 2a\sqrt 2  = \frac{{5a\sqrt 2 }}{2}(m)\).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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