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Giải bài 38 trang 75 sách bài tập toán 8 – Cánh diều

Cho tam giác \(ABC\) có \(AB = 12\)cm, \(AC = 18\)cm, \(BC = 27\)cm. Điểm \(D\) thuộc cạnh \(BC\) sao cho \(CD = 12\)cm. Tính độ dài \(AD\).

𝕴Tổng 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

Cho tam giác \(ABC\) có \(AB = 12\)cm, \(AC = 18\)cm, \(BC = 27\)cm. Điểm \(D\) thuộc cạnh \(BC\) sao cho \(CD = 12\)cm. Tính độ dài \(AD\).

Phương pháp giải - Xem chi tiết

Áp dụng trường hợp đồng dạng thứ hai của tam giác: cạnh – góc – cạnh Nếu hai cạnh của tam giác này tỉ lệ với hai cạnh của tam giác kia và hai góc tạo bởi các cặp cạnh đó bằng nhau thì hai tam giác đó đồng dạng.

Lời giải chi tiết

Do \(\frac{{AC}}{{DC}} = \frac{{18}}{{12}} = \frac{3}{2}\), \(\frac{{CB}}{{CA}} = \frac{{27}}{{18}} = \frac{3}{2}\)→    \(\frac{{AC}}{{DC}} = \frac{{CB}}{{CA}}\). Mà \(\widehat {ACB} = \widehat {ACD}\)→    \(\Delta ACB\backsim \Delta DCA\).Do đó \(\frac{{AC}}{{DC}} = \frac{{AB}}{{AD}}\) hay \(\frac{{18}}{{12}} = \frac{{12}}{{AD}}\).→    \(AD = \frac{{12.12}}{{18}} = 8\)cm.Vậy độ dài \(AD = 8\)cm.

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