10、(陕西)王师傅有两块板材边角料,其中30cm,下底为一块是边长为60cm的正方形板子;另一块是上底为30cm,下底为120cm,高为60cm的直角梯形板子(如图①).王师傅想将这两块板子裁成两块全等的矩形板材.他将两块板子叠放在一起,使梯形的两个直角顶点分别与正方形的两个顶点重合,两块板子的重叠部分为五边形ABCFE围成的区域(如图②).由于受材料纹理的限制,要求裁出的矩形要以点B为一个顶点.

   (1)求FC的长;

   (2)利用图②求出矩形顶点B所对的顶点到BC边的距离x(cm)为多少时,矩形的面积y(cm2)最大?最大面积是多少?

(3)若想使裁出的矩形为正方形,试求出面积最大的正方形的边长.

例2、[解题分析]⑴ 由

从而可得的函数表达式是

解:(1)(或)······················································ 3分

(2),又

····································································································· 5分

,即······························· 6分

解得································································ 7分

梯形的中位线长为······································································· 8分

9:分析:(1)当三角形QAP为等腰三角形时,由于∠A为直角,只能是AQ=AP,建立等量关系,,即时,三角形QAP为等腰三角形;

(2)四边形QAPC的面积=ABCD的面积-三角形QDC的面积-三角形PBC的面积

==36,即当P、Q运动时,四边形QAPC的面积不变。

(3)显然有两种情况:△PAQ∽△ABC,△QAP∽△ABC,

由相似关系得,解之得

 0  47885  47893  47899  47903  47909  47911  47915  47921  47923  47929  47935  47939  47941  47945  47951  47953  47959  47963  47965  47969  47971  47975  47977  47979  47980  47981  47983  47984  47985  47987  47989  47993  47995  47999  48001  48005  48011  48013  48019  48023  48025  48029  48035  48041  48043  48049  48053  48055  48061  48065  48071  48079  447348 

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