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Giải bài 9.11 trang 69 SGK Toán 7 tập 2 - Kết nối tri thức

a) Cho tam giác ABC có AB = 1 cm, BC = 7 cm. Hãy tìm độ dài cạnh CA biết rằng đó là một số nguyên ( cm). b) Cho tam giác ABC có AB= 2 cm, BC = 6 cm và BC là cạnh lớn nhất. Hãy tìm độ dài cạnh CA biết rằng đó là một số nguyên ( cm).

ဣTổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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Đề bài

a) Cho tam giác ABC có AB = 1 cm, BC = 7 cm. Hãy tìm độ dài cạnh CA biết rằng đó là một số nguyên ( cm). b) Cho tam giác ABC có AB= 2 cm, BC = 6 cm và BC là cạnh lớn nhất. Hãy tìm độ dài cạnh CA biết rằng đó là một số nguyên ( cm).

Phương pháp giải - Xem chi tiết

Sử dụng bất đẳng thức tam giác: Trong một tam giác, độ dài của một cạnh luôn nhỏ hơn tổng độ dài hai cạnh còn lại và lớn hơn hiệu độ dài 2 cạnh còn lại: b – c < a < b + c ( với a, b, c là độ dài 3 cạnh của tam giác) Kết hợp điều kiện độ dài cạnh CA là số nguyên

Lời giải chi tiết

a) Áp dụng bất đẳng thức tam giác trong tam giác ABC, ta có: 7 – 1 < CA < 7 + 1 6 < CA < 8 Mà CA là số nguyên CA = 7 cm. Vậy CA = 7 cm. b) Áp dụng bất đẳng thức tam giác trong tam giác ABC, ta có: AB + CA > BC 2 + CA > 6 CA > 4 cm Mà CA là số nguyên và CA < 6 ( vì BC = 6 cm là cạnh lớn nhất của tam giác)  CA = 5 cm Vậy CA = 5 cm.

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