问一道数学题

poplibaoUID: 2894543

PP2 第2套的一道题
The perimeter of square S is 40, Square T is inscribed in square S, What is the least possible area of square T?


这里面的inscribed 该怎么理解啊？ - -

星红UID: 3375235

The perimeter of square S is 40 implies each side of S is 10. The way T can be inscribed is one these two extremes: It is precisely the same square or it is a diamond in the square. If we consider the diamond, then the diagonal of that square would be 10, meaning one of the sides would have a length of 5√2 (do you know why?). Thus, the perimeter of this square T is 20√2 ≈ 28.28... therefore this square is smaller, so its area is smaller (area of square T = 50, while area of square S = 100.)

poplibaoUID: 2894543

LS这回复是粘贴复制BAIDU出来的结果吧。我看过这个解释，但还不是十分明白。 inscribed  意思是镶嵌吗？四个顶点都必须在大正方形四条边上？

poplibaoUID: 2894543

自己顶一下

worryUID: 2453376

inscribe应该就是内切的意思咯~~OG math review里面有的~~LZ再去看看~~

poplibaoUID: 2894543

worry 发表于 2012-9-18 10:14
inscribe应该就是内切的意思咯~~OG math review里面有的~~LZ再去看看~~

OK  

poplibaoUID: 2894543

worry 发表于 2012-9-18 10:14
inscribe应该就是内切的意思咯~~OG math review里面有的~~LZ再去看看~~

thanks a lot

皮皮鲁8726UID: 3367931

看2楼的意思，好像说的是：按照题目的描述T只有两种情况：一个是跟S一摸一样，另一个是S中四条边的中点为顶点组成的正方形diamond，考虑这个diamond，算出来他的周长是20倍根号2<40，而题目问的是least possible area，所以，diamond这种情况是正解。
不知道我理解的对不对