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Giải bài 14 trang 60 SGK Toán 8 tập 2– Chân trời sáng tạo

Tính độ dài

🐟Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

Tính độ dài \(x\) trong Hình 9

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Định lí đường phân giác Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn thẳng ấy.

Lời giải chi tiết

a) Xét tam giác \(ABC\) có \(AD\) là đường phân giác của \(\widehat A\). Theo định lí đường phân giác ta có: \(\frac{{BD}}{{AB}} = \frac{{DC}}{{AC}} \Leftrightarrow \frac{x}{{4,5}} = \frac{5}{{7,2}} \Rightarrow x = \frac{{4,5.5}}{{7,2}} = 3,125\) Vậy \(x = 3,125\). b) Xét tam giác \(MNP\) có \(MI\) là đường phân giác của \(\widehat M\). Theo định lí đường phân giác ta có: \(O\) \(\frac{{NI}}{{MN}} = \frac{{IP}}{{MP}} \Leftrightarrow \frac{3}{5} = \frac{{IP}}{{8,5}} \Rightarrow IP = \frac{{3.8,5}}{5} = 5,1\) Ta có: \(NP = NI + IP = 3 + 5,1 = 8,1\) Vậy \(x = 8,1\).

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