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Giải bài 5 trang 88 SGK Toán 8 tập 1– Chân trời sáng tạo

Cho hình thoi

🌃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

꧙Cho hình thoi \(ABCD\) có cạnh bằng \(13\)cm, độ dài đường chéo \(AC\) là 10cm. Độ dài đường chéo \(BD\) là:

A. 24cm B. 12cm C. 16cm D. 20cm

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng tính chất của hình thoi, Đl Pythagore

Lời giải chi tiết

Gọi \(O\) là giao điểm của hai đường chéo

Vì \(ABCD\) là hình thoi (gt) nên :

\(AC\) vuông góc với \(BD\);

\(OB = OD = \frac{1}{2}BD\);

ꦡ\(OA = OC = \frac{1}{2}AC = \frac{1}{2}.10 = 5\) (cm)

﷽Áp dụng ĐL Pythagore vào tam giác vuông \(OAB\) ta có:

ꦅ\(O{A^2} = A{B^2} - O{B^2} = {13^2} - {5^2} = 169 - 25 = 144 = {12^2}\)

\(OA = 12\) cm

Suy ra \(AC = 2OA = 2.12 = 24\) cm

Đáp án A

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