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Giải bài 22 trang 97 sách bài tập toán 8 - Cánh diều

Hình 20 mô tả mặt phẳng cắt ngang tầng trệt của một ngôi nhà. Biết \(AB \bot BC,CD \bot BC\) và \(AB = 4m,CD = 7m,AD = 11m\).

𝔉Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Hình 20 mô tả mặt phẳng cắt ngang tầng trệt của một ngôi nhà. Biết \(AB \bot BC,CD \bot BC\) và \(AB = 4m,CD = 7m,AD = 11m\). Tính độ dài \(BC\) (làm tròn kết quả đến hàng phần mười của mét).

 

Phương pháp giải - Xem chi tiết

Dựa vào tính chất của hình chữ nhật: -         Hai cạnh đối song song và bằng nhau -         Hai đường chéo bằng nhau và cắt nhau tại trung điểm của mỗi đường Và dựa vào định lí Pythagore: trong một tam giác vuông, bình phương cạnh huyền bằng tổng bình phương hai cạnh góc vuông.

Lời giải chi tiết

Kẻ \(AH\) vuông góc với \(CD\) tại \(H\) (Hình 42)Tứ giác \(ABCH\) có \(\widehat {ABC} = \widehat {BCH} = \widehat {CHA} = 90^\circ \) nên \(ABCH\) là hình chữ nhật. Suy ra \(CH = AB = 4m\)Do đó \(DH = CD - CH = 3m\)Trong tam giác \(ADH\) vuông tại \(H\), ta có:\(A{D^2} = A{H^2} + D{H^2}\)Suy ra \(A{H^2} = A{D^2} - D{H^2} = 112\)Do đó \(AH = \sqrt {112} m\)Ta có: \(BC = AH\) (vì \(ABCH\) là hình chữ nhật) nên \(BC = \sqrt {112}  \approx 10,6\left( m \right)\)

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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