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Giải bài 13 trang 63 sách bài tập toán 8 – Cánh diều

Một ngôi nhà có thiết kế mái như Hình 18 và có các số đo như sau: \(AD = 1,5\) m, \(DE = 2,5\) m, \(BF = CG = 1\) m, \(FG = 5,5\) m. Tính chiều dài \(AB\) của mái nhà, biết \(DE//BC\).

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

Một ngôi nhà có thiết kế mái như Hình 18 và có các số đo như sau: \(AD = 1,5\) m, \(DE = 2,5\) m, \(BF = CG = 1\) m, \(FG = 5,5\) m. Tính chiều dài \(AB\) của mái nhà, biết \(DE//BC\).

 

Phương pháp giải - Xem chi tiết

Áp dụng định lí Thales: Nếu một đường thẳng song song với một cạnh của tam giác và cắt hai cạnh còn lại thì nó định ra trên hai cạnh đó những đoạn thẳng tương ứng tỉ lệ.

Lời giải chi tiết

Ta có \(BC = BF + FG + GC = 7,5\)m. Do \(DE//BC\) nên theo hệ quả của định lí Thales, ta có: \(\frac{{AD}}{{AB}} = \frac{{DE}}{{BC}}\) hay \(\frac{{1,5}}{{AB}} = \frac{{2,5}}{{7,5}}\). Suy ra \(AB = 4,5\)m.

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