In this paper, a 20 cm long wire is used to encircle a rectangle. The functional relationship between the area s (CM & # 178;) and the length x (CM) of the encircled rectangle is obtained, and the value range of the independent variable x is determined

In this paper, a 20 cm long wire is used to encircle a rectangle. The functional relationship between the area s (CM & # 178;) and the length x (CM) of the encircled rectangle is obtained, and the value range of the independent variable x is determined


s=x(10-x)=-x^2+10x
Because the aspect ratio is larger and less than 10 cm, x > 10-x and X



A 20 cm long iron wire is surrounded into a rectangle, and the relationship between the area ycm2 of the rectangle and the length xcm of one side of the rectangle is given______ .


The length of the other side of the rectangle is 20 △ 2-x = 10-x, y = x (10-x) = - x2 + 10x



A 40cm long iron wire is used to form a plane figure. (1) if it is enclosed as a square, the side length is______ , with an area of______ In this case, the difference between length and width is______ (2) if it is enclosed in a rectangle with a length of 12cm, the width is______ , with an area of______ In this case, the difference between length and width is______ (3) if it is enclosed into a rectangle with a width of 5cm, the length is 5cm______ , with an area of______ In this case, the difference between length and width is______ (4) if a circle is formed, the radius of the circle is______ , with an area of______ (π is taken as 3.14, and the result is kept to one decimal place); (5) conjecture: (1) when the perimeter is constant, if the enclosed figure is a rectangle, then when the difference between the length and width is smaller and smaller, the area of the rectangle will be larger and smaller______ (fill in "big" or "small") and (2) in various plane figures surrounded by the same perimeter______ It's the largest area


(1) According to the meaning of the title, the length of the square is 40 △ 4 = 10cm, then the area is 10 × 10 = 100cm2, the difference between length and width is 10-10 = 0cm; (2) let the width be xcm, then 2 (12 + x) = 40, and the solution is x = 8, the area is 12 × 8 = 96cm2; the difference between length and width is 12-8 = 4cm; (3) let the length be YC



A square hole with a side length of 1cm is pulled out from two opposite sides of a cube wood with an edge length of 10cm. The surface area and volume of this figure are


The surface area increased by 8 square centimeters to 608 square centimeters
The volume has been reduced by 2 cubic centimeters to 998 cubic centimeters