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一、(满分20分)一片枫叶紧紧地镶嵌在一个矩形框内部,即矩形的各个边上都有枫叶边缘上的点,如图1.假设这个矩形框的每一条边都可以伸缩,令枫叶不动,矩形框转动,依靠框的伸缩始终保持这片枫叶紧紧地镶在她的内部,而框始终是矩形.请说明,存在一个转动位置,这使得这片枫叶恰紧紧地镶在一个正方形的内部.解设转动前的矩形的长和宽的长度分别为a和b.
One, (out of 20 points) Maple leaf tightly embedded in a rectangular box, that is, each side of the rectangle has a maple leaf edge points, as shown in Figure 1. Suppose the rectangular frame can stretch each side, so that the order Maple leaf does not move, the rectangular box rotation, relying on the box telescopic always keep this maple leaf tightly in her interior, and the box is always rectangular. Please note that there is a rotation position, which makes this piece of maple leaf just set Inside a square, the lengths and widths of the pre-rotation rectangle are a and b, respectively.