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问题:王大爷想用12米长的竹篱笆靠一面墙围成鸭舍,要使面积最大,应该怎么围?请你设计一个方案,画出示意图,并算出面积. 许多同学想到围成矩形,并且知道“周长相等时,正方形的面积不小于长方形面积”的规律,由此得出面积最大的方案是:围成一个正方形(如图1),一边靠墙,有三边是篱笆,每边长4米,面积是16米2. 这个方案的面积最大吗?让我们用函数的性质来分析.设矩形面积为y米2,矩形与墙面垂直的边长为x米(如图2),则与墙面平行的边长为(12-2x)米,于是y=x(12-2x)=-2x2+12x=-2(x-3)2+18.
Question: Uncle Wang wants to use a 12-metre-long bamboo fence to build a duck house by a wall. What should be the largest area to be enclosed? Please design a plan, draw a sketch, and calculate the area. Many students think of forming a rectangle. And knowing that the law of “circumference is equal to the area of the square is not smaller than the area of the rectangle”, the scheme that results in the largest area is: to form a square (see Figure 1), one side of the wall, and the other side is a fence. Each side is 4 meters long and the area is 16 meters 2. Is the area of this program the largest? Let us analyze the nature of the function. Set the area of the rectangle to y m2, and the length of the side of the rectangle perpendicular to the wall is x meters (see figure 2) The side length parallel to the wall is (12-2x) meters, so y=x(12-2x)=-2x2+12x=-2(x-3)2+18.