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Giải bài 7.29 trang 38 SGK Toán 7 tập 2 - Kết nối tri thức

Người ta dùng những chiếc cọc để rào một mảnh vườn hình chữ nhật sao cho mỗi góc vườn đều có một chiếc cọc và hai cọc liên tiếp cắm cách nhau 0,1 m. Biết rằng số cọc dùng để rào hết chiều dài của vườn nhiều hơn số cọc dùng để rào hết chiều rộng là 20 chiếc. Gọi số cọc dùng để rào hết chiều rộng là x . Tìm đa thức biểu thị diện tích của vườn đó.

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

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Đề bài

Người ta dùng những chiếc cọc để rào một mảnh vườn hình chữ nhật sao cho mỗi góc vườn đều có một chiếc cọc và hai cọc liên tiếp cắm cách nhau 0,1 m. Biết rằng số cọc dùng để rào hết chiều dài của vườn nhiều hơn số cọc dùng để rào hết chiều rộng là 20 chiếc. Gọi số cọc dùng để rào hết chiều rộng là x . Tìm đa thức biểu thị diện tích của vườn đó.

Phương pháp giải - Xem chi tiết

Biểu thị số cọc để rào hết chiều dài Tìm đa thức biểu thị chiều rộng, chiều dài. Tìm đa thức biểu thị diện tích mảnh vườn = chiều dài . chiều rộng

Lời giải chi tiết

Vì số cọc để rào hết chiều dài của vườn nhiều hơn số cọc dùng để rào hết chiều rộng là 20 chiếc nên số cọc dùng để rào chiều dài là: x + 20Do mỗi góc vườn đều có một chiếc cọc và hai cọc liên tiếp cắm cách nhau 0,1 m nên:Chiều rộng của mảnh vườn là: 0,1 . (x – 1) = 0,1x – 0,1Chiều dài của mảnh vườn là: 0,1 . (x  + 20 – 1) =  0,1(x + 19) = 0,1x + 1,9Đa thức biểu diễn diện tích mảnh vườn là:S = (0,1x – 0,1) . (0,1x + 1,9)= 0,1x . (0,1x + 1,9) – 0, 1. (0,1x + 1,9)= 0,1x . 0,1x + 0,1x . 1,9 – (0,1.0,1x + 0,1. 1,9)

= 0,01x2 + 0,19x – (0,01x + 0,19)

= 0,01x2 + 0,19x – 0,01x - 0,19

= 0,01x2 + 0,18x – 0,19

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