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Giải bài 26 trang 18 sách bài tập toán 8 - Cánh diều

Cho tam giác \(ABC\) có cạnh \(BC = 2x\left( {dm} \right)\),

ဣTổng 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 cạnh \(BC = 2x\left( {dm} \right)\), đường cao \(AH = x\left( {dm} \right)\) với \(x > 0\) và hình vuông \(MNPQ\) có cạnh \(MN = y\left( {dm} \right)\) với \(y > 0\) (Hình 4). a) Viết công thức tính tổng diện tích của các tam giác \(AMN,BMQ,CNP\) dưới dạng tích. b) Tính tổng diện tích của các tam giác \(AMN,BMQ,CNP\), biết \(x - y = 2\) và \(x + y = 10\)

Phương pháp giải - Xem chi tiết

Sử dụng công thức tính diện tích tam giác, công thức tính diện tích hình vuông và các phương pháp phân tích đa thức thành nhân tử để tính tổng diện tích các tam giác  \(AMN,BMQ,CNP\).

Lời giải chi tiết

a) Ta có:\(\begin{array}{l}{S_{AMN + BMQ + NCP}} = {S_{ABC}} - {S_{MNPQ}}\\ = \frac{1}{2}\left( {x.2x} \right) - {y^2} = {x^2} - {y^2}\\ = \left( {x - y} \right)\left( {x + y} \right)\left( {d{m^2}} \right)\end{array}\)b) Ta có:

\({S_{AMN + BMQ + NCP}} = 2.10 = 20\left( {d{m^2}} \right)\)

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