Question

中，，，cm．長(zhǎng)為1cm的線(xiàn)段在的邊上沿方向以1cm/s的速度向點(diǎn)運(yùn)動(dòng)（運(yùn)動(dòng)前點(diǎn)與點(diǎn)重合）．過(guò)分別作的垂線(xiàn)交直角邊于兩點(diǎn)，線(xiàn)段運(yùn)動(dòng)的時(shí)間為s．

（1）若的面積為，寫(xiě)出與的函數(shù)關(guān)系式（寫(xiě)出自變量的取值范圍）；

（2）線(xiàn)段運(yùn)動(dòng)過(guò)程中，四邊形有可能成為矩形嗎？若有可能，求出此時(shí)的值；若不可能，說(shuō)明理由；

（3）為何值時(shí)，以為頂點(diǎn)的三角形與相似？

Answer 1

解：（1）當(dāng)點(diǎn)在上時(shí)，，．

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

當(dāng)點(diǎn)在上時(shí)，．

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

（2），．．

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

由條件知，若四邊形為矩形，需，即，

．

當(dāng)s時(shí)，四邊形為矩形．································································ 8分

（3）由（2）知，當(dāng)s時(shí)，四邊形為矩形，此時(shí)，

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

除此之外，當(dāng)時(shí)，，此時(shí)．

，．．····························· 10分

，．

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

，．

當(dāng)s或s時(shí)，以為頂點(diǎn)的三角形與相似．·················· 12分