Question

中，，，cm．长为1cm的线段在的边上沿方向以1cm/s的速度向点运动（运动前点与点重合）．过分别作的垂线交直角边于两点，线段运动的时间为s．

（1）若的面积为，写出与的函数关系式（写出自变量的取值范围）；

（2）线段运动过程中，四边形有可能成为矩形吗？若有可能，求出此时的值；若不可能，说明理由；

（3）为何值时，以为顶点的三角形与相似？

Answer 1

解：（1）当点在上时，，．

．········································································ 2分

当点在上时，．

．·················································· 4分

（2），．．

．········································································ 6分

由条件知，若四边形为矩形，需，即，

．

当s时，四边形为矩形．································································ 8分

（3）由（2）知，当s时，四边形为矩形，此时，

．··························································································· 9分

除此之外，当时，，此时．

，．．····························· 10分

，．

又，．········································ 11分

，．

当s或s时，以为顶点的三角形与相似．·················· 12分