(2)①证明：由题意，

位似且相似比是，

.

.·································································································· 5分

又 .

.·············································································································· 7分

②的长为 .·········································································································· 9分

24.解：(1)设一张薄板的边长为 cm，它的出厂价为元，基础价为元，浮动价为元，则 . 2分

由表格中的数据，得 解得

所以 ········································································································· 4分

(2)①设一张薄板的利润为元，它的成本价为元，由题意，得

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

将代入中，得 .

解得

所以 ·························································································· 7分

②因为，所以，当(在5~50之间)时，

即出厂一张边长为25cm的薄板，获得的利润最大，最大利润是35元.························· 9分

(注：边长的取值范围不作为扣分点)

25.解：(1)，

又点在轴的正半轴上，

点的坐标为(0，3)····························································································· 2分

(2)当点在点右侧时，如图2.

若，得 .

故，此时 .································································ 4分

当点在点左侧时，如图3，由，

得，故 .

此时 .

的值为或 ······················································································· 6分

(3)由题意知，若与四边形的边相切，有以下三种情况：

①当与相切于点时，有，从而得到 .

此时 .···················································································································· 7分

②当与相切于点时，有，即点与点重合，

此时 .···················································································································· 8分

③当与相切时，由题意，，