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Thử tài bạn 7 trang 164 Tài liệu dạy – học Toán 7 tập 1

Giải bài tập 1. Tính độ dài cạnh EF, NP của tam giác vuông trong các hình 11a và 11b.
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Đề bài

1. Tính độ dài cạnh EF, NP của tam giác vuông trong các hình 11a và 11b.

 

2. Em hãy đo chiều ngang và chiều cao chiếc tivi màn hình phẳng của nhà em (đơn vị icnh). Tính độ dài đường chéo chiếc tivi đó.

 

Lời giải chi tiết

1.Tam giác DEF vuông tại D \(\Rightarrow E{F^2} = D{E^2} + D{F^2}\)   (định lí pythagore).Mà DE = 5cm (gt), DF = 12 cm (gt)Do đó: \(E{F^2} = {5^2} + {12^2} = 25 + 144 = 169;EF > 0.\)   Vậy \(EF = \sqrt {169}  = 13(cm)\)Tam giác MNP vuông tại M \(\Rightarrow N{P^2} = M{N^2} + M{P^2}\)   (định lý pythagore)Mà \(MN = \sqrt 7 cm(gt);MP = 3cm(gt)\)Do đó: \(N{P^2} = {\left( {\sqrt 7 } \right)^2} + {3^2} = 7 + 9 = 16,NP > 0.\)   Vậy \(NP = \sqrt {16}  = 4(cm).\)2.Chiếc tivi màn hình phẳng của nhà em có chiều ngang 40 inchGọi độ dài đường chéo tivi đó là d (inch).Theo định lí pythagore ta có:\({d^2} = {40^2} + {30^2} \Rightarrow {d^2} = 1600 + 900 = 2500\)Mà d > 0. Vậy \(d = \sqrt {2500}  = 50(inch)\)Độ dài đường chéo chiếc tivi đó là 50 (inch).

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