摘要：如图12.直角梯形中..动点从点出发.沿方向移动.动点从点出发.在边上移动．设点移动的路程为.点移动的路程为.线段平分梯形的周长． (1)求与的函数关系式.并求出的取值范围, (2)当时.求的值, (3)当不在边上时.线段能否平分梯形的面积?若能.求出此时的值,若不能.说明理由． 解:(1)过作于.则.可得. 所以梯形的周长为18．·············································································· 1分 平分的周长.所以.····························································· 2分 因为.所以. 所求关系式为:．·············· 3分 (2)依题意.只能在边上.． . 因为.所以.所以.得··························· 4分 .即. 解方程组 得．··················································· 6分 (3)梯形的面积为18．············································································· 7分 当不在边上.则. ()当时.在边上.． 如果线段能平分梯形的面积.则有········································· 8分 可得:解得(舍去)．·········································· 9分 ()当时.点在边上.此时． 如果线段能平分梯形的面积.则有. 可得此方程组无解． 所以当时.线段能平分梯形的面积．········································· 11分

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