解答它---Here is the extracted content from the image: **Problem Description:** 25. (10分) 如图1, 直线AB: $y=\frac{3}{4}x+6$ 与直线CD $y=-\frac{1}{2}x+1$ 交于点C, 直线CD与y轴交于点E. **(1)** 求$\triangle BDE$的周长; **(2)** 如图2, 点K为直线CD上-动点, 点T为x轴上-动点, 连接BK, TK, 若点K在第四象限, 且$S_{\triangle KBD}=\frac{2}{3}S_{\triangle ACD}$, 求$KT+\frac{1}{2}AT$的最小值及此时点T的坐标; **(3)** 如图3, 将直线CD沿y轴向下平移使其经过点A得到直线AF, 若点P、点Q在直线AB上运动 (点P在点Q右侧), 点R在直线AF上运动, 若以点P、Q、R、E为顶点的四边形为矩形, 直接写出点R的坐标及对应的线段PQ的长度. **Diagram Descriptions:** * **图1:** * Type: Cartesian coordinate system with two intersecting lines. * Coordinate Axes: X-axis and Y-axis intersecting at origin O. Positive directions indicated by arrows. * Lines: * Line AB: Upward sloping line intersecting the Y-axis at B and the X-axis at some point left of O, labeled A. Point C is the intersection of line AB and line CD. Point E is on line CD and the Y-axis. Point D is the intersection of line CD and the X-axis. * Line CD: Downward sloping line intersecting the Y-axis at E and the X-axis at D. * Points: A, B, C, D, E, O. Point B is on the Y-axis. Point A and D are on the X-axis. * Labels: O (origin), A, B, C, D, E, x (x-axis), y (y-axis). * **图2:** * Type: Cartesian coordinate system with two intersecting lines and additional points. * Coordinate Axes: X-axis and Y-axis intersecting at origin O. Positive directions indicated by arrows. * Lines: * Line AB: Same as in 图1, passing through A, C, B. * Line CD: Same as in 图1, passing through C, E, D. * Points: A, B, C, D, E, O. Also includes points T and K. * Point T is on the X-axis. * Point K is on line CD. It is shown in the fourth quadrant. * Lines BK and TK are drawn. * Labels: O (origin), A, B, C, D, E, T, K, x (x-axis), y (y-axis). * **图3:** * Type: Cartesian coordinate system with three lines and multiple points. * Coordinate Axes: X-axis and Y-axis intersecting at origin O. Positive directions indicated by arrows. * Lines: * Line AB: Same as in 图1 and 图2, passing through Q, P, C, B. * Line CD: Same as in 图1 and 图2, passing through C, E, D. * Line AF: A new line, shown as parallel to line CD and passing through point A. Point R and F are on this line. * Points: A, B, C, D, E, O. Also includes points P, Q, R, F. * Points P and Q are on line AB, with P to the right of Q. * Point R is on line AF. * Point F is on line AF and the X-axis. * Labels: O (origin), A, B, C, D, E, P, Q, R, F, x (x-axis), y (y-axis). * **备用图 (Spare Diagram):** * Type: Cartesian coordinate system with three lines and multiple points. * Coordinate Axes: X-axis and Y-axis intersecting at origin O. Positive directions indicated by arrows. * Lines: * Line AB: Similar to the other diagrams, passing through C, B. * Line CD: Similar to the other diagrams, passing through C, E, D. * A third line, labeled AF, parallel to CD and passing through A and F. * Points: A, B, C, D, E, O, F. * Labels: O (origin), A, B, C, D, E, F, x (x-axis), y (y-axis).